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At… | bartleby</title><script type="application/ld+json">{ "@context": "https://schema.org", "@type": [ "QAPage", "WebPage" ], "mainEntityOfPage": { "@type": "WebPage", "@id": "https://www.bartleby.com/questions-and-answers/the-acceleration-of-a-particle-moving-only-on-a-horizontal-xy-plane-is-given-by-a-2ti-3t-where-a-is-/6323b717-25e7-4c51-9d84-a3ef975392e1" }, "name": "The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits", "description": "The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits", "inLanguage": "en", "headline": "The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits", "datePublished": "2023-02-23", "dateModified": "2023-02-23", "isAccessibleForFree": "False", "hasPart": { "@type": "WebPageElement", "isAccessibleForFree": "False", "cssSelector": ".paywall" }, "mainEntity": { "@type": "Question", "name": "The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits", "text": "The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits", "answerCount": 1, "dateCreated": "2023-02-23", "acceptedAnswer": { "@type": "Answer", "text": "Answered: Image /qna-images/answer/6323b717-25e7-4c51-9d84-a3ef975392e1.jpg" }, "url": "https://www.bartleby.com/questions-and-answers/the-acceleration-of-a-particle-moving-only-on-a-horizontal-xy-plane-is-given-by-a-2ti-3t-where-a-is-/6323b717-25e7-4c51-9d84-a3ef975392e1" } }</script><script type="application/ld+json">{ "@context": "http://schema.org/", "@type": "VideoObject", "name": " The acceleration of a particle moving only on a horizontal xy plane i", "description": " The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 31ĵ, where a is in meters per second-squared and t is in seconds. 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At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits</div></div></div><div class="styles__H1TextWithContentFlagging-sc-b909a4b8-12 eRvBJb"><h1 class="styles__H1Text-sc-b909a4b8-9 hbescp">The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits</h1><span class="styles__ContentFlagging-sc-b909a4b8-13 hzcRRH"><img src="/static/flag-icon.svg" alt="Report"/></span></div></div></div></div></div></div><main role="main" id="bartleby-main" class="styles__AppLayoutScrollableContainer-sc-ef9b07f2-5 caxWVm"><div id="qa_ad_top" class="TopAdSlot__TopAdSlotContainer-sc-11874efb-0 fVfOtq"></div><div id="APP_LAYOUT_RAILS_CONTAINER_ID" class="styles__AppLayoutMainContentOuterWrapper-sc-ef9b07f2-6 ZpaTT"><div class="styles__AppLayoutWrapperWithPadding-sc-ef9b07f2-7 styles__AppLayoutMainContentInnerWrapper-sc-ef9b07f2-10 fzyfgw irHRkV"><div class="styles__AppLayoutBaseRailWithMargins-sc-ef9b07f2-13 styles__AppLayoutMainContentLeftToTopRotationRail-sc-ef9b07f2-14 ewrpEf fqCnEe"><div class="styles__RightRailAddContainer-sc-b00d20a1-7 jUtlCD"><div class="styles__RightRailSectionContainer-sc-b00d20a1-0 jUDevz"><div class="styles__RailContainerSection-sc-b00d20a1-6 ctdPFO"><div id="TEXTBOOK-MODULE-ID" class="styles__TextBookModuleContainer-sc-f621c991-0 kzwzwE"><div id="book-meta-info" role="region" aria-labelledby="expand-collapse-btns" class="styles__TextBookModuleExpandedContainer-sc-f621c991-1 kGKCTW"><div class="styles__BookMetaWrapper-sc-9504037c-8 Pkmsn"><a href="https://amzn.to/4791Ipj" target="_blank" class="styles__BookMetaHref-sc-9504037c-14 RyA-Df"><span class="styles__BuyButtonParentWrapper-sc-fe125262-0 styles__BuyButtonWrapper-sc-9504037c-12 eihJbg XOIcj"><img src="https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif" alt="College Physics" loading="lazy" decoding="async" class="styles__BookImage-sc-9504037c-1 jmvJbr"/><button class="SegmentAnalyticsButton__ButtonWithNoStyle-sc-bd08475e-0 jZeIgm GhostButton-sc-2b1a9e6a-0 styles__BookBuyButton-sc-9504037c-0 kEdpZh fKFSYj">BUY</button></span></a><div class="styles__BookTitleAndBookMarkContainer-sc-9504037c-11 gjtOzU"><a href="/textbooks/college-physics-11th-edition/9781305952300/solutions" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__BookTitle-sc-9504037c-2 dQfard">College Physics </a><div class="styles__BookMetaContainer-sc-9504037c-3 geSXFb"><div class="styles__BookMetaItems-sc-9504037c-4 kpIAHE"><span class="styles__BookMetaEdition-sc-9504037c-5 btydzX">11th Edition</span><div class="styles__BookMetaBoldItem-sc-9504037c-6 gDfNjy">ISBN: <span class="styles__BookMetaLightItem-sc-9504037c-7 iEzPCN">9781305952300</span></div><div class="styles__BookMetaBoldItem-sc-9504037c-6 gDfNjy">Author: Raymond A. Serway, Chris Vuille</div><div class="styles__BookMetaBoldItem-sc-9504037c-6 gDfNjy">Publisher: <span class="styles__BookMetaLightItem-sc-9504037c-7 iEzPCN">Cengage Learning</span></div></div></div></div><div class="styles__BookmarkWrapper-sc-9504037c-9 jaYaPx"><button aria-label="Book information" aria-haspopup="true" class="styles__ExpandCollapseButton-sc-9504037c-13 eWtESO"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__CollapseIcon-sc-9504037c-10 fHHDSb material-icons">expand_less</i></button></div></div><div id="CHAPTER-AND-PROBLEM-CONTAINER-ID" class="styles__ChapterAndProblemContainer-sc-6c5678b1-0 gWOZUA"><div class="VerticalSpacer-sc-2377adbb-0 kiWBPl"></div><div class="styles__SelectDropdownWrapper-sc-6c5678b1-1 eOyBMf"><div class="Select__SelectContainer-sc-834a2da0-0 fxCyOA"><div class="Select__LabelAndIconContainer-sc-834a2da0-1 dJyRFP"><label for="chapter-list" class="InputLabel__Label-sc-47bf7b53-0 lkTNwl"></label></div><div class="VerticalSpacer-sc-2377adbb-0 hqoCAi"></div><div class="Select__SelectAndArrowDownWrapper-sc-834a2da0-3 cygoKT"><select title="1 Units, Trigonometry. And Vectors" id="chapter-list" aria-label="chapter list" class="Select__StyledSelect-sc-834a2da0-2 gSyoDW"><option value="0" selected="">1 Units, Trigonometry. And Vectors</option><option value="1">2 Motion In One Dimension</option><option value="2">3 Motion In Two Dimensions</option><option value="3">4 Newton's Laws Of Motion</option><option value="4">5 Energy</option><option value="5">6 Momentum, Impulse, And Collisions</option><option value="6">7 Rotational Motion And Gravitation</option><option value="7">8 Rotational Equilibrium And Dynamics</option><option value="8">9 Fluids And Solids</option><option value="9">10 Thermal Physics</option><option value="10">11 Energy In Thermal Processes</option><option value="11">12 The Laws Of Thermodynamics</option><option value="12">13 Vibrations And Waves</option><option value="13">14 Sound</option><option value="14">15 Electric Forces And Fields</option><option value="15">16 Electrical Energy And Capacitance</option><option value="16">17 Current And Resistance</option><option value="17">18 Direct-Current Circuits</option><option value="18">19 Magnetism</option><option value="19">20 Induced Voltages And Inductance</option><option value="20">21 Alternating-Current Circuits And Electromagnetic Waves</option><option value="21">22 Reflection And Refraction Of Light</option><option value="22">23 Mirrors And Lenses</option><option value="23">24 Wave Optics</option><option value="24">25 Optical Instruments</option><option value="25">26 Relativity</option><option value="26">27 Quantum Physics</option><option value="27">28 Atomic Physics</option><option value="28">29 Nuclear Physics</option><option value="29">30 Nuclear Energy And Elementary Particles</option></select><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl Select__ArrowDownIcon-sc-834a2da0-4 kiottc material-icons">expand_more</i></div></div><div class="Select__SelectContainer-sc-834a2da0-0 fxCyOA"><div class="Select__LabelAndIconContainer-sc-834a2da0-1 dJyRFP"><label for="section-list" class="InputLabel__Label-sc-47bf7b53-0 lkTNwl"></label></div><div class="VerticalSpacer-sc-2377adbb-0 hqoCAi"></div><div class="Select__SelectAndArrowDownWrapper-sc-834a2da0-3 cygoKT"><select title="Chapter Questions" id="section-list" aria-label="section list" class="Select__StyledSelect-sc-834a2da0-2 gSyoDW"><option value="0">1.1 Standards Of Length, Mass, And Time</option><option value="1">1.2 The Building Blocks Of Matter</option><option value="2">1.3 Dimensional Analysis</option><option value="3">1.4 Uncertainty In Measurement And Significant Figures</option><option value="4">1.5 Unit Conversions For Physical Quantities</option><option value="5">1.6 Estimates And Order-of-Magnitude Calculations</option><option value="6">1.7 Coordinate Systems</option><option value="7">1.8 Trigonometry Review</option><option value="8">1.9 Vectors</option><option value="9">1.10 Cornoonentsofavector</option><option value="10">1.11 Problem-Solving Strategy</option><option value="11" selected="">Chapter Questions</option></select><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl Select__ArrowDownIcon-sc-834a2da0-4 kiottc material-icons">expand_more</i></div></div></div><div class="VerticalSpacer-sc-2377adbb-0 hqoCAi"></div><div class="Select__SelectContainer-sc-834a2da0-0 fxCyOA"><div class="Select__LabelAndIconContainer-sc-834a2da0-1 dJyRFP"><label for="problem-list" class="InputLabel__Label-sc-47bf7b53-0 lkTNwl"></label></div><div class="VerticalSpacer-sc-2377adbb-0 hqoCAi"></div><div class="Select__SelectAndArrowDownWrapper-sc-834a2da0-3 cygoKT"><select id="problem-list" aria-label="problem list" class="Select__StyledSelect-sc-834a2da0-2 gSyoDW"><option value="0" selected="">Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...</option><option value="1">Problem 2CQ: What types of natural phenomena could serve as time standards?</option><option value="2">Problem 3CQ: Find the order of magnitude of your age in seconds.</option><option value="3">Problem 4CQ: An object with a mass of 1 kg weighs approximately 2 lb. Use this information to estimate the mass...</option><option value="4">Problem 5CQ: (a) Estimate the number of times your heart beats in a month, (b) Estimate the number of human...</option><option value="5">Problem 6CQ: Estimate the number of atoms in 1 cm5 of a solid. (Note that the diameter of an atom is about 1010...</option><option value="6">Problem 7CQ: Lacking modern timepieces, early experimenters some-times measured time intervals with their pulse....</option><option value="7">Problem 8CQ</option><option value="8">Problem 9CQ</option><option value="9">Problem 10CQ: List some advantages of the metric system of units over most other systems of units.</option><option value="10">Problem 11CQ: Estimate the time duration of each of the following in the suggested units in parentheses: (a) a...</option><option value="11">Problem 12CQ: Suppose two quantities, A and B, have different dimensions. Determine which of the following...</option><option value="12">Problem 13CQ: Answer each question yes or no. Must two quantities have the same dimensions (a) if you are adding...</option><option value="13">Problem 14CQ: Two different measuring devices are used by students to measure the length of a metal rod. Students...</option><option value="14">Problem 15CQ: If B is added to A, under what conditions does the resultant vector have a magnitude equal to A + B?...</option><option value="15">Problem 16CQ: Under what circumstances would a vector have components that are equal in magnitude?</option><option value="16">Problem 1P: The period of a simple pendulum, defined as the time necessary for one complete oscillation, is...</option><option value="17">Problem 2P: (a) Suppose the displacement of an object is related to time according to the expression x = Bt2....</option><option value="18">Problem 3P: A shape that covers an area A and has a uniform height h has a volume V = Ah. (a) Show that V = Ah...</option><option value="19">Problem 4P: Each of the following equations was given by a student during an examination: (a) 12mv2=12mv02+mgh...</option><option value="20">Problem 5P</option><option value="21">Problem 6P: Kinetic energy KE (Topic 5) has dimensions kg m2/s2. It can be written in terms of the momentum p...</option><option value="22">Problem 7P: A rectangular airstrip measures 32.30 in by 210 m, with the width measured more accurately than the...</option><option value="23">Problem 8P: Use the rules for significant figures to find the answer to the addition problem 21.4 + 15 + 17.17 +...</option><option value="24">Problem 9P: A carpet is to be installed in a room of length 9.72 m and width 5.3 m. Find the area of the mom...</option><option value="25">Problem 10P</option><option value="26">Problem 11P: How many significant figures are there in (a) 78.9 0.2, (b) 3.788 109, (c) 2.46 1026, (d) 0.003 2</option><option value="27">Problem 12P: The speed of light is now defined to be 2.997 924 58 108 m/s. Express the speed of light to (a)...</option><option value="28">Problem 13P: A rectangle has a length of (2.0 0.2) m and a width of (1.5 0.1) m. Calculate (a) the area and (b)...</option><option value="29">Problem 14P: The radius of a circle is measured to be (10.5 0.2) m. Calculate (a) the area and (b) the...</option><option value="30">Problem 15P: The edges of a shoebox are measured to be 11.4 cm, 17.8 cm, and 29 cm. Determine the volume of the...</option><option value="31">Problem 16P: Carry out the following arithmetic operations: (a) the sum of the measured values 756, 37.2, 0.83,...</option><option value="32">Problem 17P: The Roman cubitus is an ancient unit of measure equivalent to about 0.445 m. Convert the 2.00m...</option><option value="33">Problem 18P: A house is advertised as having 1 420 square feet under roof. What is the area of this house in...</option><option value="34">Problem 19P: A fathom is a unit of length, usually reserved for measuring the depth of water. A fathom is...</option><option value="35">Problem 20P: A small turtle moves at a speed of 186 furlongs per fortnight. Find the speed of the turtle in...</option><option value="36">Problem 21P: A firkin is an old British unit of volume equal to 9 gallons. How many cubic meters are there in...</option><option value="37">Problem 22P: Find the height or length of these natural wonders in kilometers, meters, and centimeters: (a) The...</option><option value="38">Problem 23P: A car is traveling at a speed of 38.0 m/s on an interstate high-way where the speed limit is 75.0...</option><option value="39">Problem 24P: A certain car has a fuel efficiency of 25.0 miles per gallon (mi/gal). Express this efficiency in...</option><option value="40">Problem 25P: The diameter of a sphere is measured to be 5.36 in. Find (a) the radius of the sphere in...</option><option value="41">Problem 26P: Suppose your hair grows at the rate of 1/32 inch per day. Find the rate at which it grows in...</option><option value="42">Problem 27P: The speed of light is about 3.00 108 m/s. Convert this figure to miles per hour.</option><option value="43">Problem 28P: A house is 50.0 ft long and 26 ft wide and has 8.0-ft-high ceilings. What is the volume of the...</option><option value="44">Problem 29P: The amount of water in reservoirs is often measured in acre-ft. One acre-ft is a volume that covers...</option><option value="45">Problem 30P: The base of a pyramid covers an area of 13.0 acres (1 acre = 43 560 ft2) and has a height of 481 ft...</option><option value="46">Problem 31P: A quart container of ice cream is to be made in the form of a cube. What should be the length of a...</option><option value="47">Problem 32P: Estimate the number of steps you would have to take to walk a distance equal to the circumference of...</option><option value="48">Problem 33P: Estimate the number of breaths taken by a human being during an average lifetime.</option><option value="49">Problem 34P: Estimate the number of people in the world who are suffering from the common cold on any given day....</option><option value="50">Problem 35P: The habitable part of Earths surface has been estimated to cover 60 trillion square meters. Estimate...</option><option value="51">Problem 36P: Treat a cell in a human as a sphere of radius 1.0 m. (a) Determine the volume of a cell. (b)...</option><option value="52">Problem 37P: An automobile tire is rated to last for 50 000 miles. Estimate the number of revolutions the tire...</option><option value="53">Problem 38P: A study from the National Institutes of Health stales that the human body contains trillions of...</option><option value="54">Problem 39P: A point is located in a polar coordinate system by the coordinates r = 2.5 m and = 35. Find the x-...</option><option value="55">Problem 40P: A certain corner of a room is selected as the origin of a rectangular coordinate system. If a fly is...</option><option value="56">Problem 41P: Express the location of the fly in Problem 40 in polar coordinates.</option><option value="57">Problem 42P: Two points in a rectangular coordinate system have the coordinates (5.0, 3.0) and (3.0, 4.0), where...</option><option value="58">Problem 43P: Two points are given in polar coordinates by (r, ) = (2.00 m, 50.0) and (r, ) = (5.00 m, 50.0),...</option><option value="59">Problem 44P: Given points (r1, 1) and (r2, 2) in polar coordinates, obtain a general formula for the distance...</option><option value="60">Problem 45P: For the triangle shown in Figure P1.45, what are (a) the length of the unknown side, (b) the tangent...</option><option value="61">Problem 46P: A ladder 9.00 m long leans against the side of a building. If the ladder is inclined at an angle of...</option><option value="62">Problem 47P: A high fountain of water is located at the center of a circular pool as shown in Figure P1.47. Not...</option><option value="63">Problem 48P: A right triangle has a hypotenuse of length 3.00 m, and one of its angles is 30.0. What are the...</option><option value="64">Problem 49P: In Figure P1.49, find (a) the side opposite , (b) the side adjacent to . (c) cos , (d) sin , and (c)...</option><option value="65">Problem 50P: In a certain right triangle, the two sides that are perpendicular to each other are 5.00 m and 7.00...</option><option value="66">Problem 51P: In Problem 50, what is the tangent of the angle for which 5.00 in is the opposite side?</option><option value="67">Problem 52P: A woman measures the angle of elevation of a mountaintop as 12.0. After walking 1.00 km closer to...</option><option value="68">Problem 53P: A surveyor measures the distance across a straight river by the following method: starting directly...</option><option value="69">Problem 54P: Vector A has a magnitude of 8.00 units and makes an angle of 45.0 with the positive x-axis. Vector B...</option><option value="70">Problem 55P: Vector A has a magnitude of 29 units and points in the positive y-direction. When vector B is added...</option><option value="71">Problem 56P: An airplane flies 2.00 102 km due west from city A to city B and then 3.00 102 km in the direction...</option><option value="72">Problem 57P: Vector A is 3.00 units in length and points along the positive x-axis. Vector B is 4.00 units in...</option><option value="73">Problem 58P: A force F1, of magnitude 6.00 units acts on an object at the origin in a direction = 30.0 above the...</option><option value="74">Problem 59P: A roller coaster moves 2.00 102 ft horizontally and then rises 135 ft at an angle of 30.0 above the...</option><option value="75">Problem 60P: Calculate (a) the x-component and (b) the y-component of the vector with magnitude 24.0 m and...</option><option value="76">Problem 61P: A vector A has components Ax = 5.00 m and Ay = 9.00 m. Find (a) the magnitude and (b) the direction...</option><option value="77">Problem 62P: A person walks 25.0 north of east for 3.10 km. How far due north and how far due east would she have...</option><option value="78">Problem 63P: The magnitude of vector A is 35.0 units and points in the direction 325 counterclockwise from the...</option><option value="79">Problem 64P: A figure skater glides along a circular path of radius 5.00 m. If she coasts around one half of the...</option><option value="80">Problem 65P: A girl delivering newspapers covers her route by traveling 3.00 blocks west, 4.00 blocks north, and...</option><option value="81">Problem 66P: A quarterback takes the ball from the line of scrimmage, runs backwards for 10.0 yards, and then...</option><option value="82">Problem 67P: A vector has an x-component of 25.0 units and a y-component of 40.0 units. Find the magnitude and...</option><option value="83">Problem 68P: A map suggests that Atlanta is 730. miles in a direction 5.00 north of east from Dallas. The same...</option><option value="84">Problem 69P: The eye of a hurricane passes over Grand Bahama Island in a direction 60.0 north of west with a...</option><option value="85">Problem 70P: The helicopter view in Figure P1.70 shows two people pulling on a stubborn mule. Find (a) the single...</option><option value="86">Problem 71P: A commuter airplane starts from an airport and takes the route shown in Figure P1.71. The plane...</option><option value="87">Problem 72AP: (a) Find a conversion factor to convert from miles per hour to kilometers per hour. (b) For a while,...</option><option value="88">Problem 73AP: The displacement of an object moving under uniform acceleration is some function of time and the...</option><option value="89">Problem 74AP: Assume it takes 7.00 minutes to fill a 30.0-gal gasoline tank. (a) Calculate the rate at which the...</option><option value="90">Problem 75AP: One gallon of paint (volume = 3.79 103 m3) covers an area of 25.0 m2. What is the thickness of the...</option><option value="91">Problem 76AP: A sphere of radius r has surface area A = 4r2 and volume V = (4/3)r3. If the radius of sphere 2 is...</option><option value="92">Problem 77AP: Assume there are 100 million passenger can in the United States and that the average fuel...</option><option value="93">Problem 78AP</option><option value="94">Problem 80AP: An average person sneezes about three times per day. Estimate the worldwide number of sneezes...</option><option value="95">Problem 81AP: The nearest neutron star (a collated star made primarily of neutrons) is about 3.00 1018 m away...</option></select><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl Select__ArrowDownIcon-sc-834a2da0-4 kiottc material-icons">format_list_bulleted</i></div></div><div class="VerticalSpacer-sc-2377adbb-0 iLgLps"></div></div><div><div id="SEE-SIMILAR-BOOK-WRAPPER-ID" class="styles__SeeSimilarBookWrapper-sc-14a32097-0 dWrLRy"><div class="styles__SeeSimilarBookText-sc-14a32097-2 eoIkYi"><a href="/subject/science/physics/textbook-answers" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm StandaloneLink__StandaloneLinkElement-sc-dc6ff55b-0 gyBeu">See similar textbooks</a></div></div></div></div></div><div class="styles__RelatedQuestionsContainer-sc-7afe3f32-16 dHsHSE"><div class="styles__CommonImageContainerWrapper-sc-7afe3f32-25 dwuEpY"><div class="styles__RelatedQuestionsImageContainer-sc-7afe3f32-18 iZWohG"><img width="15" height="15" src="/static/leftrail/relatedQuestions.svg" alt="Bartleby Related Questions Icon" class="styles__RelatedQuestionsImage-sc-7afe3f32-19 ffmpeW"/></div><h4 tabindex="0" aria-label="Related questions" class="styles__RelatedQuestionsShowTitle-sc-7afe3f32-17 eTpGbX">Related questions</h4></div><button aria-label="open related questions" id="related-question-left-rail" aria-expanded="false" aria-controls="related-question-panel" class="SegmentAnalyticsButton__ButtonWithNoStyle-sc-bd08475e-0 jZeIgm UnstyledButton-sc-362851bc-0 ibfVkD"><img width="10" height="5" src="/static/leftrail/expandButton.svg" alt="Bartleby Expand Icon" class="styles__ExpandArrow-sc-7afe3f32-3 dBnLxf"/></button></div><div id="related-question-panel" aria-labelledby="#related-question-left-rail" class="styles__LeftRailPreview-sc-7afe3f32-4 evbBaW"><div class="styles__RelatedSections-sc-7afe3f32-6 sgRcD"><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/a-what-is-the-magnitude-in-km-and-direction-in-degrees-south-of-east-of-her-displacement-during-the-/0ef2afd9-cd6e-4763-9442-41b1ef0a490b" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: (a) What is the magnitude (in km) and direction (in degrees south of east) of her displacement…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: The distance moved by the person towards the south, The distance moved by the person toward the…</div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/a-car-moves-along-a-horizonatal-road-with-constant-velocity-v-0-v-0-xi-i-30.06-msi-until-it-encounte/108a153f-458e-46ed-b486-2ec083fc5c08" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: A car moves along a horizonatal road with constant velocityv0 = v0, x^ii = (30.06 m/s)^i until it…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: The objective of the question is to find the average acceleration of the car during the given time…</div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/problem-17-a-mountain-biker-encounters-a-jump-on-a-race-course-that-sends-him-into-the-air-at-43.1-d/14a87303-4bb5-4397-8f21-81d5380e2397" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: Problem 17: A mountain biker encounters a jump on a race course that sends him into the air at 43.1…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: </div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/in-the-figure-a-baseball-is-hit-at-a-height-h-1.30-m-and-then-caught-at-the-same-height.-it-travels-/1673e39b-2618-4431-8c8d-f6ab9e710c2b" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: In the figure, a baseball is hit at a height h = 1.30 m and then caught at the same height. 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The ball is 20.1 m from the goalpost. The ball is…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: </div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/a-particle-leaves-the-origin-with-an-initial-velocity-7.83i-ms-and-a-constant-acceleration-a-1.38i-2/56edfee8-a745-4e6a-a91a-a1b078779aaa" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: A particle leaves the origin with an initial velocity = (7.83î) m/s and a constant acceleration à =…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: </div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/the-position-vector-of-a-particle-moving-in-the-xy-plane-is-given-by-at-bt-r-where-t-is-the-time-in-/5fb0b6ac-800f-4871-8c30-de49876a7f17" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: The position vector of a particle moving in the xy-plane is given by (At, Bt¹) r = where t is the…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: Given:Position vector:r= (4.5t, 8.0t4) a) Magnitude of particle displacement at t = 2 s:r = (4.5t,…</div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/the-acceleration-vector-of-a-particle-is-giving-bya-27-t2jms4.-the-particle-is-located-at-the-origin/60faa43b-4bdb-4c14-a335-503f8f840d1a" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: The acceleration vector of a particle is giving by a = -27 t2 j m/s4. The particle is located at…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: </div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/at-time-t-0-the-position-vector-of-a-particle-moving-in-the-x-y-plane-is-r-5.80i-m.-by-time-t-0.016-/614f1e53-4953-4139-b323-5ac355626acd" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: At time t = 0, the position vector of a particle moving in the x-y plane is r = 5.80i m. By time t =…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: </div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/a-particle-r-2t3-3t-i-4-5t2-j-t4-k-position-depending-on-time-given-position-moves-with-the-vector.-/61bd0bee-1f62-40ea-a9b3-52c65ee9d31e" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: A particle r = (2t3+ 3t) i + (4 - 5t2) j - t4 k Position depending on time given position moves with…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: Given quantities: position vector (r) = ( 2t3 + 3t ) i + ( 4 - 5t2 ) j - t4 k Let, the distance…</div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/the-vector-position-of-a-particle-varies-in-time-according-to-the-expression-r-20ti2-20t-5t-2j-m-a-f/652a0e58-4462-4b5a-9b1f-88d4198c5b10" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: The vector position of a particle varies in time according to the expression: r =( 20ti+(2 + 20t-5t…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: The position vector of the particle is given as: r→=20t i^+2+20t-5t2j^ It is required to find its…</div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/a-soccer-ball-is-punted-from-the-ground-at-an-angle-theta-42-degrees-with-respect-to-the-horizontal./75aa0036-9c0c-4ef2-8892-a4be5509dda5" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: A soccer ball is punted from the ground at an angle theta = 42 degrees with respect to the…</div></div><div class="styles__RelatedQuestionsItemContent-sc-7afe3f32-24 hTqbEo">A: </div></a></div><div class="styles__RelatedQuestionsItemContainer-sc-7afe3f32-20 iqXVGf"><a href="/questions-and-answers/eters-per-second.-a-for-that-6.20-s-what-is-the-protons-average-acceleration-a-avg-in-unit-vector-no/782b2933-2af0-4be5-8472-02e0a0de8ffc" class="BaseAnchorElementWithDisabledState__AnchorWithDisabledState-sc-4e9e1c9d-0 kMhnvm styles__RelatedQuestionsLink-sc-7afe3f32-21 jYuRoD"><div class="styles__RelatedQuestionsItemHeader-sc-7afe3f32-23 cklByt"><div class="styles__RelatedQuestionsItemTitle-sc-7afe3f32-22 bbpOLQ">Q: eters per second). 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class="styles__ConceptExplainerItemHeader-sc-7afe3f32-14 diZwOL"><div class="styles__ConceptExplainerItemTitle-sc-7afe3f32-13 bDLomE">Projectile Motion</div></div><div class="styles__ConceptExplainerItemContent-sc-7afe3f32-15 dqKJrs"></div></a></div></div></div></div></div><div class="styles__QnaTopicVideoWrapper-sc-f1329b46-1 bywekk"><div class="styles__QnaTopicVideoHeader-sc-f1329b46-2 kQhFNT">Topic Video</div><button class="styles__QnaTopicVideoSection-sc-f1329b46-3 gWhkVv"></button></div><div id="qa_ad_sidebar" class="SidebarAdSlot__SidebarAdSlotContainer-sc-ef295d43-0 kuFPZn"></div></div></div><div class="styles__AppLayoutMainContentMiddleRail-sc-ef9b07f2-11 fFewXf"><div class="styles__MyQuestionsPageContainer-sc-ff0bc2ab-5 fjSEwR"><div id="qna-answer-container-id" data-bby-tooltip-parent-container="true" class="styles__MyQuestionWithAnswerContainer-sc-70138c7b-0 feRSfh"><div class="styles__QuestionWithAnswerContainer-sc-3354f32b-0 iwINRK"><div class="styles__QuestionHeadingContainer-sc-3354f32b-23 cQzfmR"><div class="DisplayOnThresholdCss__DivDisplayContainer-sc-ad524cbe-0 fhOrnX"><div class="styles__QuestionPraticeShareContainer-sc-3354f32b-24 gkoRXy"><div class="styles__ShareSolutionForMobile-sc-3354f32b-25 dbqwxV"></div></div></div><div class="styles__QuestionHeadingWithShareSolution-sc-3354f32b-22 fYRcWH"><div class="styles__QuestionHeaderWrapper-sc-3354f32b-1 Qgpse"><div role="heading" aria-level="2" data-section-name="Question" class="styles__QuestionHeader-sc-3354f32b-6 iPWTwc">Question</div></div><div class="DisplayOnThresholdCss__DivDisplayContainer-sc-ad524cbe-0 bNInGa"></div></div></div><div class="DisplayOnThresholdCss__DivDisplayContainer-sc-ad524cbe-0 BUCpX"></div></div><div class="styles__MyQuestionContainer-sc-3a2a762c-0 cmXtQz"><figure class="styles__MyQuestionImageContainer-sc-89bde9a8-0 fwYStS"><div class="styles__MyQuestionImageInnerContainer-sc-89bde9a8-2 ecucAc"><picture><source media="(min-width: 376px)" srcSet="https://content.bartleby.com/qna-images/question/4c2c149f-9455-4f49-9292-1c1375ef6171/6323b717-25e7-4c51-9d84-a3ef975392e1/5f57b7_processed.png"/><img alt="The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 31ĵ, where a is in meters per second- squared and t is in seconds. At t = 0, the position vector = (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector 7 = (6.40m/s)i + (3.20m/s) j. At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number i (b) Number i î+ Units i ĴUnits" height="295" width="970" src="https://content.bartleby.com/qna-images/question/4c2c149f-9455-4f49-9292-1c1375ef6171/6323b717-25e7-4c51-9d84-a3ef975392e1/5f57b7_thumbnail.png" class="styles__PictureFallbackImage-sc-6028e6d3-0 beMLwO"/></picture><div class="styles__MyQuestionExpandButtonWrapper-sc-89bde9a8-1 fyQVDJ"><div class="styles__ZoomImageIconWrapper-sc-89bde9a8-7 emfwSv"><img src="/static/expand-img.svg" alt="expand button" loading="lazy" decoding="async" class="styles__MyQuestionZoomImg-sc-89bde9a8-6 jEbNTi"/></div></div></div><div class="styles__TranscribedImageWrapper-sc-89bde9a8-3 gfBtSw"><span class="styles__TranscribedImageHead-sc-89bde9a8-4 fJiMfh">Transcribed Image Text:</span><span class="styles__TranscribedImageText-sc-89bde9a8-5 ifjzhJ">The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 31ĵ, where a is in meters per second- squared and t is in seconds. At t = 0, the position vector = (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector 7 = (6.40m/s)i + (3.20m/s) j. At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number i (b) Number i î+ Units i ĴUnits</span></div></figure></div> <div id="Expert-Solution" class="styles__MyAnswerWrapper-sc-251af6e9-0 dpodmi paywall"><div class="styles__QuestionWithAnswerContainer-sc-3354f32b-0 iwINRK"><div class="styles__QuestionHeadingContainer-sc-3354f32b-23 cQzfmR"><div class="DisplayOnThresholdCss__DivDisplayContainer-sc-ad524cbe-0 fhOrnX"><div class="styles__QuestionPraticeShareContainer-sc-3354f32b-24 gkoRXy"><div class="styles__ShareSolutionForMobile-sc-3354f32b-25 dbqwxV"></div></div></div><div class="styles__QuestionHeadingWithShareSolution-sc-3354f32b-22 fYRcWH"><div class="styles__QuestionHeaderWrapper-sc-3354f32b-1 iUpVmK"><div role="heading" aria-level="2" data-section-name="Expert Solution" class="styles__QuestionHeader-sc-3354f32b-6 iPWTwc">Expert Solution</div><img alt="Check Mark" width="24" height="24" src="/static/check-mark.png" decoding="async"/></div><div class="DisplayOnThresholdCss__DivDisplayContainer-sc-ad524cbe-0 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Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) what are the car’s position vectors at these two times? (b) what is the car’s displacement between 0 min and 6.0 min?</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/a-ball-is-shot-from-the-ground-into-the-air.-at-a-height-of-9.4-m-its-velocity-is-7.71-6.2-ms-with-i/a34e35eb-50ec-4655-bd04-312138844a19" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">A ball is shot from the ground into the air. At a height of 9.4 m, its velocity is = 7.71+ 6.27 m/s, with i horizontal and upward. (a) To what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? What are the (c) magnitude and (d) angle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground?</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/given-the-displacement-vector-3.12-2.0-0-a-what-is-the-position-of-the-object-at-time-2.1-assuming-t/a39f5961-1d1d-4590-be87-912dc892c8c6" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">Given the displacement vector ? =[3.1?2, 2.0?, 0]:(a) what is the position of the object at time? = 2.1 ? assuming the object started at theorigin?(b) what is the distance the object has traveled at? = 2.1 ??(c) what is the velocity of the object as a functionof time?(d) what is the velocity of the object at ? = 0, ? =2.1 ? and ? = 4.2 ??(e) what is the speed of the object at the timesgiven in part (d). Are the speed evenly spaced?Would you expect this? Why or why not?(f) what is the acceleration of the object at? = 0, ? = 2.1 ? and ? = 4.2 ??</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a></div></li><li class="styles__CarouselSlide-sc-99cce645-3 jJOhIn"><div class="styles__SimilarQuestionsContainer-sc-45f7b23f-0 fUFRAY"><a href="/questions-and-answers/at-t-0-a-stone-is-thrown-at-an-angle-of-35.0-above-the-horizontal-with-an-initial-speed-equal-to-25./b3ec2cff-4a47-466b-8269-4ce5f76a44aa" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">At t = 0, a stone is thrown at an angle of 35.0 ◦ above the horizontal with an initial speed equal to 25.0 ms−1. Calculate the magnitudes of the horizontal and vertical components of its displacement at t = 1.20 s.</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/a-plane-flies-493-km-east-from-city-a-to-city-b-in-45.0-min-and-then-983-km-south-from-city-b-to-cit/b520393e-1c6e-4440-a315-e480ffe2ead2" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">A plane flies 493 km east from city A to city B in 45.0 min and then 983 km south from city B to city C in 1.30 h. For the total trip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its average velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180 degrees, measured from the +x direction (east). (a) Number i Units (b) Number Units (c) Number i Units (d) Number i Units (e) Number Units II</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/a-particle-travels-along-the-following-vectors-in-succession-d1-5i-d2-12j-and-d3-2i-4j-and-d4-6i-5j./b784c9f7-c84b-47ce-b0e3-6a1fcc40b201" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">Please asap</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a></div></li><li class="styles__CarouselSlide-sc-99cce645-3 jJOhIn"><div class="styles__SimilarQuestionsContainer-sc-45f7b23f-0 fUFRAY"><a href="/questions-and-answers/a-particle-leaves-the-origin-with-an-initial-velocity-3.00i-ms-and-a-constant-acceleration-a-1.00i-0/ce370336-73fa-495d-8095-1097c9f0248c" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">A particle leaves the origin with an initial velocity 3.00î m/s and a constant acceleration ở -1.00î – 0.50ĵ m/s². When it reaches its maximum x coordinate, what are its (a) velocity and (b) position vector?</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/a-proton-initially-has-7.10i-5.10-6.60-a.-6.60-and-then-2.70-s-later-has-7-4.70-5.10-13.0-i-meters-p/cec75a84-284b-4d17-8012-6d7f9802d493" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">A proton initially has 7 = (-7.10)î + (5.10)Ƒ + (−6.60)î : and then 2.70 s later has 7 = (4.70)î + (5.10)ĵ + (13.0)ê (in avg meters per second). (a) For that 2.70 s, what is the proton's average acceleration a in unit vector notation, (b) in magnitude, and the angle between a and the positive direction of the x axis? avg (a) Number i 11.8 (b) Number i (c) Number i î+ Units Units i 19.6 k Units m/s</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/a-snowmobile-is-originally-at-the-point-with-position-vector30.5m-at-95.0counterclockwise-from-the-x/d6391a6c-1fbc-4540-8d6f-49dc7b64ec89" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">A snowmobile is originally at the point with position vector 30.5 m at 95.0° counterclockwise from the x-axis, moving with velocity 4.89 m/s at 40.0°. It moves with a constant acceleration 1.72 m/s2 at 200°. After 5.00 s have elapsed, find the following. (Express your answers in vector form.) (a) its velocity vector. (b) its position vector.</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a></div></li><li class="styles__CarouselSlide-sc-99cce645-3 jJOhIn"><div class="styles__SimilarQuestionsContainer-sc-45f7b23f-0 fUFRAY"><a href="/questions-and-answers/an-ions-position-vector-is-initially-7-9.1-2.4-m-i-7.4-7-number-i-1-m-i-i-9.9-m-7.4-m-6.5-m-.-in-10-/d9dc340a-ede5-408b-af1f-56e068e93048" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">Number An ion's position vector is initially 7 = (2.4 m )î + (−7.4 m )3 + (6.5 m ). In unit-vector notation, what is its average velocity during the 6.7 s? )ĵ i 1 + = 9.1 m )i + (−9.9 m )ĵ + (−10 m )k, ) + (-10 m ), and 6.7 s later it is -0.37313433 Ĵ + MI -2.46268657 k Units m/s</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/a-particle-initially-located-at-the-origin-has-an-acceleration-of-a-2.00-ms-and-an-initial-velocity-/dcfba911-fc46-4724-868b-9df074dcc135" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">A particle initially located at the origin has an acceleration of a = 2.00ĵ m/s² and an initial velocity of = 6.00î m/s. (a) Find the vector position of the particle at any time t (where t is measured in seconds). ( tî + (²ĵ) m f (b) Find the velocity of the particle at any time t. ( î+ tj) m/s (c) Find the coordinates of the particle at t = 7.00 s. X = y = m m (d) Find the speed of the particle at t = 7.00 s. m/s Submit Answer</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a><a href="/questions-and-answers/given-the-position-vector-~rt-t2itj-in-meters-what-is-the-magnitude-of-the-velocity-vector-at-a-time/e1beedbe-bec9-4c79-8f94-e2f9864c7b2e" class="styles__QuestionContentLink-sc-45f7b23f-5 dMPDtR"><div class="styles__QuestionCardContainer-sc-45f7b23f-1 eqtjaq"><div class="styles__QuestionLeftSection-sc-45f7b23f-2 bkfJRF"><div class="styles__QuestionContent-sc-45f7b23f-4 gsybQb">Given the position vector ~r(t) = t^2ˆi+tˆj in meters, what is the magnitudeof the velocity vector at a time of three seconds?</div></div><div class="styles__QuestionRightSection-sc-45f7b23f-3 dYdKMA"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__ArrowForward-sc-45f7b23f-6 jlyWFI material-icons">arrow_forward</i></div></div></a></div></li></ul><div class="styles__CarouselIndicatorWrapper-sc-99cce645-4 euMTlS"><div class="styles__CarouselIconIndicator-sc-99cce645-5 fEcmCJ"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__CarouselArrows-sc-99cce645-0 sRcuh material-icons">arrow_back_ios</i></div><ul class="styles__CarouselIndicators-sc-99cce645-6 iRLBYO"><li class="styles__CarouselIndicator-sc-1836a7cb-12 iZrNsj"></li><li class="styles__CarouselIndicator-sc-1836a7cb-12 dMkVi"></li><li class="styles__CarouselIndicator-sc-1836a7cb-12 dMkVi"></li><li class="styles__CarouselIndicator-sc-1836a7cb-12 dMkVi"></li></ul><div tabindex="0" role="link" class="styles__SeeMoreQuestions-sc-99cce645-1 iNqFGN">SEE MORE QUESTIONS</div><div class="styles__CarouselIconIndicator-sc-99cce645-5 fEcmCJ"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__CarouselArrows-sc-99cce645-0 sRcuh material-icons">arrow_forward_ios</i></div></div></div></div><div class="styles__RecommendedTextBooksWrapper-sc-e38ba66-18 gGmLCV"><div class="styles__SimilarQuestionWrapper-sc-e38ba66-16 ePBahg"><div role="heading" aria-level="2" class="styles__CommonHeading-sc-e38ba66-10 cGaLBm">Recommended textbooks for you</div><div class="styles__SimilarQuestionsCarouselArrow-sc-e38ba66-15 HhudC"><button aria-label="Previous items" class="SegmentAnalyticsButton__ButtonWithNoStyle-sc-bd08475e-0 jZeIgm UnstyledButton-sc-362851bc-0 ibfVkD"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__CarouselArrows-sc-e38ba66-17 gopSFY material-icons">arrow_back_ios</i></button><button aria-label="Next items" class="SegmentAnalyticsButton__ButtonWithNoStyle-sc-bd08475e-0 jZeIgm UnstyledButton-sc-362851bc-0 ibfVkD"><i aria-hidden="true" class="Icon__IconStyledComponent-sc-4e7587c2-0 diHyLl styles__CarouselArrows-sc-e38ba66-17 gopSFY material-icons">arrow_forward_ios</i></button></div></div><ul class="styles__RecommendedTextBooksInnerContainer-sc-847e36a9-1 jQArXr"><li class="styles__CarouselSlideRecommondedTextBook-sc-847e36a9-2 jLCAvi"><div class="styles__RecommondedTextBookCarouselContainer-sc-847e36a9-3 bEoEQQ"><div class="styles__SingleTextBookWrapper-sc-ca3c9c92-2 jlaAYV"><div class="styles__TextBookContainerWrapper-sc-ca3c9c92-4 cdXMcV"><img src="https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif" alt="Text book image" loading="lazy" decoding="async" class="styles__TextBookImageContainer-sc-ca3c9c92-3 blkA-Dv"/><div class="styles__TextBookContentWrapper-sc-ca3c9c92-5 bfDgdN"><a href="/textbooks/college-physics-11th-edition/9781305952300/solutions" class="styles__TextBookTitle-sc-ca3c9c92-6 dhFyfM">College Physics</a><div class="styles__ChildSubjectContent-sc-ca3c9c92-7 hJsptO"><div class="styles__ConceptExplainerItemTagIndicator-sc-ca3c9c92-0 eliTei"><div class="styles__ConceptExplainerItemTagInnerPoint-sc-ca3c9c92-1 DCysr"></div></div>Physics</div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">ISBN:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">9781305952300</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Author:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Raymond A. 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Adams, Gina Brissenden</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Publisher:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Addison-Wesley</span></div></div></div></div><div class="styles__SingleTextBookWrapper-sc-ca3c9c92-2 jlaAYV"><div class="styles__TextBookContainerWrapper-sc-ca3c9c92-4 cdXMcV"><img src="https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif" alt="Text book image" loading="lazy" decoding="async" class="styles__TextBookImageContainer-sc-ca3c9c92-3 blkA-Dv"/><div class="styles__TextBookContentWrapper-sc-ca3c9c92-5 bfDgdN"><a href="/textbooks/college-physics-a-strategic-approach-4th-edition-4th-edition/9780134609034/solutions" class="styles__TextBookTitle-sc-ca3c9c92-6 dhFyfM">College Physics: A Strategic Approach (4th Editio...</a><div class="styles__ChildSubjectContent-sc-ca3c9c92-7 hJsptO"><div class="styles__ConceptExplainerItemTagIndicator-sc-ca3c9c92-0 eliTei"><div class="styles__ConceptExplainerItemTagInnerPoint-sc-ca3c9c92-1 DCysr"></div></div>Physics</div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">ISBN:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">9780134609034</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Author:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Randall D. 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Serway, Chris Vuille</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Publisher:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Cengage Learning</span></div></div></div></div><div class="styles__SingleTextBookWrapper-sc-ca3c9c92-2 jlaAYV"><div class="styles__TextBookContainerWrapper-sc-ca3c9c92-4 cdXMcV"><img src="https://www.bartleby.com/isbn_cover_images/9780133969290/9780133969290_smallCoverImage.gif" alt="Text book image" loading="lazy" decoding="async" class="styles__TextBookImageContainer-sc-ca3c9c92-3 blkA-Dv"/><div class="styles__TextBookContentWrapper-sc-ca3c9c92-5 bfDgdN"><a href="/textbooks/university-physics-14th-edition-14th-edition/9780133969290/solutions" class="styles__TextBookTitle-sc-ca3c9c92-6 dhFyfM">University Physics (14th Edition)</a><div class="styles__ChildSubjectContent-sc-ca3c9c92-7 hJsptO"><div class="styles__ConceptExplainerItemTagIndicator-sc-ca3c9c92-0 eliTei"><div class="styles__ConceptExplainerItemTagInnerPoint-sc-ca3c9c92-1 DCysr"></div></div>Physics</div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">ISBN:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">9780133969290</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Author:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Hugh D. 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Serway, John W. Jewett</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Publisher:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Cengage Learning</span></div></div></div></div><div class="styles__SingleTextBookWrapper-sc-ca3c9c92-2 jlaAYV"><div class="styles__TextBookContainerWrapper-sc-ca3c9c92-4 cdXMcV"><img src="https://www.bartleby.com/isbn_cover_images/9780321820464/9780321820464_smallCoverImage.gif" alt="Text book image" loading="lazy" decoding="async" class="styles__TextBookImageContainer-sc-ca3c9c92-3 blkA-Dv"/><div class="styles__TextBookContentWrapper-sc-ca3c9c92-5 bfDgdN"><a href="/textbooks/lecture-tutorials-for-introductory-astronomy-3rd-edition/9780321820464/solutions" class="styles__TextBookTitle-sc-ca3c9c92-6 dhFyfM">Lecture- Tutorials for Introductory Astronomy</a><div class="styles__ChildSubjectContent-sc-ca3c9c92-7 hJsptO"><div class="styles__ConceptExplainerItemTagIndicator-sc-ca3c9c92-0 eliTei"><div class="styles__ConceptExplainerItemTagInnerPoint-sc-ca3c9c92-1 DCysr"></div></div>Physics</div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">ISBN:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">9780321820464</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Author:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Edward E. Prather, Tim P. Slater, Jeff P. Adams, Gina Brissenden</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Publisher:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Addison-Wesley</span></div></div></div></div><div class="styles__SingleTextBookWrapper-sc-ca3c9c92-2 jlaAYV"><div class="styles__TextBookContainerWrapper-sc-ca3c9c92-4 cdXMcV"><img src="https://www.bartleby.com/isbn_cover_images/9780134609034/9780134609034_smallCoverImage.gif" alt="Text book image" loading="lazy" decoding="async" class="styles__TextBookImageContainer-sc-ca3c9c92-3 blkA-Dv"/><div class="styles__TextBookContentWrapper-sc-ca3c9c92-5 bfDgdN"><a href="/textbooks/college-physics-a-strategic-approach-4th-edition-4th-edition/9780134609034/solutions" class="styles__TextBookTitle-sc-ca3c9c92-6 dhFyfM">College Physics: A Strategic Approach (4th Editio...</a><div class="styles__ChildSubjectContent-sc-ca3c9c92-7 hJsptO"><div class="styles__ConceptExplainerItemTagIndicator-sc-ca3c9c92-0 eliTei"><div class="styles__ConceptExplainerItemTagInnerPoint-sc-ca3c9c92-1 DCysr"></div></div>Physics</div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">ISBN:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">9780134609034</span></div><div class="styles__TextBookContent-sc-ca3c9c92-8 kvHvmd"><span class="styles__TextBookContentHead-sc-ca3c9c92-9 deUnwS">Author:</span><span class="styles__TextBookContentText-sc-ca3c9c92-10 imOqmn">Randall D. 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At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity\nvector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between\nits direction of travel and the positive direction of the x axis?\n(a) Number\nMi\n(b) Number i\nî+\nUnits\ni\nĴUnits","topicTaxonomy":[{"id":2253,"title":"Projectile motion","shortName":"projectile-motion","externalSystemPath":"Kinematics/Motion in 2-D/Projectile motion","question_topic_taxonomy_assoc":{"id":"d22b98a9-b3a6-11ed-9ab8-0ee78e503865","question_id":"6323b717-25e7-4c51-9d84-a3ef975392e1","question_type":"QNA","topic_taxonomy_id":2253,"created_date":"2023-02-23T18:20:59.000Z"}}],"answeredDate":"2023-02-23T18:20:58.000Z","hasMicroExplainers":false,"microExplainersData":[]},"answer":{"id":"7528a3e8-b5f7-4620-957e-e6ff3667ab56","status":"Accepted","questionId":"6323b717-25e7-4c51-9d84-a3ef975392e1","createdDate":"2023-02-23T18:20:58.000Z","steps":[{"sequence":"0","header":"Step 1","text":"\u003cp\u003e\u003cimg src=\"https://prod-qna-question-images.s3.amazonaws.com/qna-images/answer/4c2c149f-9455-4f49-9292-1c1375ef6171/7528a3e8-b5f7-4620-957e-e6ff3667ab56/5w0z2k.jpg\" alt=\"Physics homework question answer, step 1, image 1\" /\u003e\u003c/p\u003e"}],"rejectionMessage":null,"imagesProcessed":0,"primaryRejectionReason":null,"secondaryRejectionReason":null,"numberOfAnswerSteps":1,"schemaAnswerSteps":"Answered: Image /qna-images/answer/6323b717-25e7-4c51-9d84-a3ef975392e1.jpg","previewAnswer":true,"hasMicroExplainers":false,"certified":false,"hasVideo":false},"isOwned":false,"isRestricted":false,"exactMatch":null,"parentQuestion":null,"isBlocked":false,"followUpQuestions":[],"defaultTopicAdded":false,"inReview":false,"isUnlocked":false,"practicePacks":[],"solutionSummaryDetails":{"imagesCount":4,"stepsCount":4,"hasVideo":false,"isPopular":false,"aiSummary":null},"isAiResponse":false,"isAiResponseAccepted":null,"answerSource":"ROUTER","fullAnswerDisplayed":false,"isGoogleBot":false},"questionProgress":"","feedbackOptions":[],"feedbackState":null,"stepsFeedbackState":[],"qnaQuestionAnswerZippies":[{"answer":"The distance moved by the person towards the south, The distance moved by the person toward the…","id":"0ef2afd9-cd6e-4763-9442-41b1ef0a490b","questionText":"(a) What is the magnitude (in km) and direction (in degrees south of east) of her displacement…","slug":"a-what-is-the-magnitude-in-km-and-direction-in-degrees-south-of-east-of-her-displacement-during-the-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=0ef2afd9-cd6e-4763-9442-41b1ef0a490b","as":"/questions-and-answers/a-what-is-the-magnitude-in-km-and-direction-in-degrees-south-of-east-of-her-displacement-during-the-/0ef2afd9-cd6e-4763-9442-41b1ef0a490b"}}},{"answer":"The objective of the question is to find the average acceleration of the car during the given time…","id":"108a153f-458e-46ed-b486-2ec083fc5c08","questionText":"A car moves along a horizonatal road with constant velocityv0 = v0, x^ii = (30.06 m/s)^i\n \nuntil it…","slug":"a-car-moves-along-a-horizonatal-road-with-constant-velocity-v-0-v-0-xi-i-30.06-msi-until-it-encounte","computed":{"hrefAndAs":{"href":"/my-questions?questionId=108a153f-458e-46ed-b486-2ec083fc5c08","as":"/questions-and-answers/a-car-moves-along-a-horizonatal-road-with-constant-velocity-v-0-v-0-xi-i-30.06-msi-until-it-encounte/108a153f-458e-46ed-b486-2ec083fc5c08"}}},{"answer":"","id":"14a87303-4bb5-4397-8f21-81d5380e2397","questionText":"Problem 17: A mountain biker encounters a jump on a race course that sends him into the air at 43.1…","slug":"problem-17-a-mountain-biker-encounters-a-jump-on-a-race-course-that-sends-him-into-the-air-at-43.1-d","computed":{"hrefAndAs":{"href":"/my-questions?questionId=14a87303-4bb5-4397-8f21-81d5380e2397","as":"/questions-and-answers/problem-17-a-mountain-biker-encounters-a-jump-on-a-race-course-that-sends-him-into-the-air-at-43.1-d/14a87303-4bb5-4397-8f21-81d5380e2397"}}},{"answer":"This question is based on oblique projectile motion.","id":"1673e39b-2618-4431-8c8d-f6ab9e710c2b","questionText":"In the figure, a baseball is hit at a height h = 1.30 m and then caught at the same height. 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and an initial…","slug":"a-particle-initially-located-at-the-origin-has-an-acceleration-of-a-2.00j-ms-and-an-initial-velocity","computed":{"hrefAndAs":{"href":"/my-questions?questionId=4d7d7359-7e79-442a-abcd-b50c547afa98","as":"/questions-and-answers/a-particle-initially-located-at-the-origin-has-an-acceleration-of-a-2.00j-ms-and-an-initial-velocity/4d7d7359-7e79-442a-abcd-b50c547afa98"}}},{"answer":"Given,\n The launched angle of the soccer ball is θ = 530 ( with respect to the horizontal ) \nThe…","id":"4f714847-7504-424d-85fd-785570de1f93","questionText":"Problem 3: A soccer ball is kicked from the ground at an angle of 0 = 53 degrees with respect to the…","slug":"problem-3-a-soccer-ball-is-kicked-from-the-ground-at-an-angle-of-0-53-degrees-with-respect-to-the-ho","computed":{"hrefAndAs":{"href":"/my-questions?questionId=4f714847-7504-424d-85fd-785570de1f93","as":"/questions-and-answers/problem-3-a-soccer-ball-is-kicked-from-the-ground-at-an-angle-of-0-53-degrees-with-respect-to-the-ho/4f714847-7504-424d-85fd-785570de1f93"}}},{"answer":"Solution:-Given thatInitial velocity (u→)=(7.8 j^) m/sacceleration (a→)=(4.4 i^+3 j^) m/s2x…","id":"5314eb63-94dc-455d-8766-f41fb27cf2db","questionText":"A particle starts from the origin at t = 0 with a\nvelocity of 7.8 and moves in the xy plane with a…","slug":"a-particle-starts-from-the-origin-at-t-0-with-a-velocity-of-7.8-and-moves-in-the-xy-plane-with-a-con","computed":{"hrefAndAs":{"href":"/my-questions?questionId=5314eb63-94dc-455d-8766-f41fb27cf2db","as":"/questions-and-answers/a-particle-starts-from-the-origin-at-t-0-with-a-velocity-of-7.8-and-moves-in-the-xy-plane-with-a-con/5314eb63-94dc-455d-8766-f41fb27cf2db"}}},{"answer":"","id":"5536a135-de2d-42e5-81e0-b7188c477c5f","questionText":"A placekicker is about to kick a field goal. The ball is 20.1 m from the goalpost. The ball is…","slug":"a-placekicker-is-about-to-kick-a-field-goal.-the-ball-is-20.1-m-from-the-goalpost.-the-ball-is-kicke","computed":{"hrefAndAs":{"href":"/my-questions?questionId=5536a135-de2d-42e5-81e0-b7188c477c5f","as":"/questions-and-answers/a-placekicker-is-about-to-kick-a-field-goal.-the-ball-is-20.1-m-from-the-goalpost.-the-ball-is-kicke/5536a135-de2d-42e5-81e0-b7188c477c5f"}}},{"answer":"","id":"56edfee8-a745-4e6a-a91a-a1b078779aaa","questionText":"A particle leaves the origin with an initial velocity = (7.83î) m/s and a constant acceleration à =…","slug":"a-particle-leaves-the-origin-with-an-initial-velocity-7.83i-ms-and-a-constant-acceleration-a-1.38i-2","computed":{"hrefAndAs":{"href":"/my-questions?questionId=56edfee8-a745-4e6a-a91a-a1b078779aaa","as":"/questions-and-answers/a-particle-leaves-the-origin-with-an-initial-velocity-7.83i-ms-and-a-constant-acceleration-a-1.38i-2/56edfee8-a745-4e6a-a91a-a1b078779aaa"}}},{"answer":"Given:Position vector:r= (4.5t, 8.0t4) a) Magnitude of particle displacement at t = 2 s:r = (4.5t,…","id":"5fb0b6ac-800f-4871-8c30-de49876a7f17","questionText":"The position vector of a particle moving in the xy-plane is given by\n(At, Bt¹)\nr =\nwhere t is the…","slug":"the-position-vector-of-a-particle-moving-in-the-xy-plane-is-given-by-at-bt-r-where-t-is-the-time-in-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=5fb0b6ac-800f-4871-8c30-de49876a7f17","as":"/questions-and-answers/the-position-vector-of-a-particle-moving-in-the-xy-plane-is-given-by-at-bt-r-where-t-is-the-time-in-/5fb0b6ac-800f-4871-8c30-de49876a7f17"}}},{"answer":"","id":"60faa43b-4bdb-4c14-a335-503f8f840d1a","questionText":"The acceleration vector of a particle is giving by a = -27 t2 j m/s4. The particle is located at…","slug":"the-acceleration-vector-of-a-particle-is-giving-bya-27-t2jms4.-the-particle-is-located-at-the-origin","computed":{"hrefAndAs":{"href":"/my-questions?questionId=60faa43b-4bdb-4c14-a335-503f8f840d1a","as":"/questions-and-answers/the-acceleration-vector-of-a-particle-is-giving-bya-27-t2jms4.-the-particle-is-located-at-the-origin/60faa43b-4bdb-4c14-a335-503f8f840d1a"}}},{"answer":"","id":"614f1e53-4953-4139-b323-5ac355626acd","questionText":"At time t = 0, the position vector of a particle moving in the x-y plane is r = 5.80i m. By time t =…","slug":"at-time-t-0-the-position-vector-of-a-particle-moving-in-the-x-y-plane-is-r-5.80i-m.-by-time-t-0.016-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=614f1e53-4953-4139-b323-5ac355626acd","as":"/questions-and-answers/at-time-t-0-the-position-vector-of-a-particle-moving-in-the-x-y-plane-is-r-5.80i-m.-by-time-t-0.016-/614f1e53-4953-4139-b323-5ac355626acd"}}},{"answer":"Given quantities:\nposition vector (r) = ( 2t3 + 3t ) i + ( 4 - 5t2 ) j - t4 k\n \nLet, the distance…","id":"61bd0bee-1f62-40ea-a9b3-52c65ee9d31e","questionText":"A particle r = (2t3+ 3t) i + (4 - 5t2) j - t4 k Position depending on time given position\nmoves with…","slug":"a-particle-r-2t3-3t-i-4-5t2-j-t4-k-position-depending-on-time-given-position-moves-with-the-vector.-","computed":{"hrefAndAs":{"href":"/my-questions?questionId=61bd0bee-1f62-40ea-a9b3-52c65ee9d31e","as":"/questions-and-answers/a-particle-r-2t3-3t-i-4-5t2-j-t4-k-position-depending-on-time-given-position-moves-with-the-vector.-/61bd0bee-1f62-40ea-a9b3-52c65ee9d31e"}}},{"answer":"The position vector of the particle is given as:\nr→=20t i^+2+20t-5t2j^\nIt is required to find its…","id":"652a0e58-4462-4b5a-9b1f-88d4198c5b10","questionText":"The vector position of a particle varies in time according to the expression: r =( 20ti+(2 + 20t-5t…","slug":"the-vector-position-of-a-particle-varies-in-time-according-to-the-expression-r-20ti2-20t-5t-2j-m-a-f","computed":{"hrefAndAs":{"href":"/my-questions?questionId=652a0e58-4462-4b5a-9b1f-88d4198c5b10","as":"/questions-and-answers/the-vector-position-of-a-particle-varies-in-time-according-to-the-expression-r-20ti2-20t-5t-2j-m-a-f/652a0e58-4462-4b5a-9b1f-88d4198c5b10"}}},{"answer":"","id":"75aa0036-9c0c-4ef2-8892-a4be5509dda5","questionText":"A soccer ball is punted from the ground at an angle theta = 42 degrees with respect to the…","slug":"a-soccer-ball-is-punted-from-the-ground-at-an-angle-theta-42-degrees-with-respect-to-the-horizontal.","computed":{"hrefAndAs":{"href":"/my-questions?questionId=75aa0036-9c0c-4ef2-8892-a4be5509dda5","as":"/questions-and-answers/a-soccer-ball-is-punted-from-the-ground-at-an-angle-theta-42-degrees-with-respect-to-the-horizontal./75aa0036-9c0c-4ef2-8892-a4be5509dda5"}}},{"answer":"","id":"782b2933-2af0-4be5-8472-02e0a0de8ffc","questionText":"eters per second). 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At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits","description":"The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits","inLanguage":"en","headline":"The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits","datePublished":"2023-02-23","dateModified":"2023-02-23","isAccessibleForFree":"False","hasPart":{"@type":"WebPageElement","isAccessibleForFree":"False","cssSelector":".paywall"},"mainEntity":{"@type":"Question","name":"The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits","text":"The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits","answerCount":1,"dateCreated":"2023-02-23","acceptedAnswer":{"@type":"Answer","text":"Answered: Image /qna-images/answer/6323b717-25e7-4c51-9d84-a3ef975392e1.jpg"},"url":"https://www.bartleby.com/questions-and-answers/the-acceleration-of-a-particle-moving-only-on-a-horizontal-xy-plane-is-given-by-a-2ti-3t-where-a-is-/6323b717-25e7-4c51-9d84-a3ef975392e1"}},"qnaAnswerFeedbackStats":{"numberOfUpVotes":0,"numberOfDownVotes":0,"numberOfStars":null,"shouldShowRating":false,"pageViews":null},"breadcrumbXmlSchemaData":{"@context":"http://schema.org","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https://www.bartleby.com/","name":"Bartleby Textbook Solutions"}},{"@type":"ListItem","position":2,"item":{"@id":"https://www.bartleby.com/subject/science","name":"Science Q\u0026A and Textbook Solutions"}},{"@type":"ListItem","position":3,"item":{"@id":"https://www.bartleby.com/subject/science/physics","name":"Physics Q\u0026A, Textbooks, and Solutions"}},{"@type":"ListItem","position":4,"item":{"@id":"https://www.bartleby.com/subject/science/physics/questions-and-answers","name":"Physics Q\u0026A Library"}},{"@type":"ListItem","position":5,"item":{"@id":"https://www.bartleby.com/questions-and-answers/the-acceleration-of-a-particle-moving-only-on-a-horizontal-xy-plane-is-given-by-a-2ti-3t-where-a-is-/6323b717-25e7-4c51-9d84-a3ef975392e1","name":"The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits"}}]},"qnAAggregateRatingXmlSchemaData":null,"solutionVideoXmlSchemaData":null,"topicVideoXmlSchemaData":{"@context":"http://schema.org/","@type":"VideoObject","name":" The acceleration of a particle moving only on a horizontal xy plane i","description":" The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 31ĵ, where a is in meters per second-squared and t is in seconds. 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Particles","sequenceText":"30","solutionsAvailable":true,"isChapterLevel":true}]}],"isBookshelved":false,"isFree":false,"bookId":"c0e7bc4d-3f7d-11e8-a3e8-a45d36699311","textBookUrl":"https://amzn.to/4791Ipj","bookmarks":[],"stickyHeaderProps":{"centerText":"The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits"},"breadcrumbParts":[{"name":"Science","shouldShrinkSlowly":true,"breadcrumbLink":{"hrefAndAs":{"href":{"pathname":"/subject","query":{"subject":"science"}},"as":"/subject/science"},"onClickGtmEvent":{"event":"Clicked on Q\u0026A Solution Breadcrumb","location":{"name":"Q\u0026A Solution Page"}}}},{"name":"Physics","shouldShrinkSlowly":true,"breadcrumbLink":{"hrefAndAs":{"href":{"pathname":"/subSubject","query":{"subject":"science","subSubject":"physics"}},"as":"/subject/science/physics"},"onClickGtmEvent":{"event":"Clicked on Q\u0026A Solution Breadcrumb","location":{"name":"Q\u0026A Solution Page"}}}},{"name":"The acceleration of a particle moving only on a horizontal xy plane is given by a = 2tî + 3t), where a is in meters per second- squared and t is in seconds. At t = 0, the position vector 7= (23.0m)i + (47.0m) locates the paticle, which then has the velocity vector = (6.40m/s)i + (3.20m/s). At t = 4.60 s, what are (a) its position vector in unit-vector notation and (b) the angle between its direction of travel and the positive direction of the x axis? (a) Number Mi (b) Number i î+ Units i ĴUnits","shouldShrinkSlowly":false}],"solutionId":"b5107875-98d6-11e8-ada4-0ee91056875a","queryChapterOrSection":false,"dcsRecommendationData":{"items":[{"type":"QNA","answerText":"Given data: \nInitial position of car = 3.0 km west of traffic light\nAt t = 0\nFinal position = 7.0 km east of traffic light\nAt t = 8.0 min\nLight at origin, +x direction is eastward","questionId":"9e3a4e50-e01a-4e01-b564-6e10ba1376e1","questionText":"A car is 3.0 km west of a traffic light at t = 0 and 7.0 km east of the light at t = 8.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) what are the car’s position vectors at these two times? (b) what is the car’s displacement between 0 min and 6.0 min?","slug":"a-car-is-3.0-km-west-of-a-traffic-light-at-t-0-and-7.0-km-east-of-the-light-at-t-8.0-min.-assume-the","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=9e3a4e50-e01a-4e01-b564-6e10ba1376e1","as":"/questions-and-answers/a-car-is-3.0-km-west-of-a-traffic-light-at-t-0-and-7.0-km-east-of-the-light-at-t-8.0-min.-assume-the/9e3a4e50-e01a-4e01-b564-6e10ba1376e1"},"content":"A car is 3.0 km west of a traffic light at t = 0 and 7.0 km east of the light at t = 8.0 min. Assume the origin of the coordinate system is the light and the positive x direction is eastward. (a) what are the car’s position vectors at these two times? (b) what is the car’s displacement between 0 min and 6.0 min?"}},{"type":"QNA","answerText":"","questionId":"a34e35eb-50ec-4655-bd04-312138844a19","questionText":"A ball is shot from the ground into the air. At a height of 9.4 m, its velocity is = 7.71+ 6.27 m/s, with i horizontal and upward. (a)\nTo what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? What are the (c) magnitude and (d)\nangle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground?","slug":"a-ball-is-shot-from-the-ground-into-the-air.-at-a-height-of-9.4-m-its-velocity-is-7.71-6.2-ms-with-i","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=a34e35eb-50ec-4655-bd04-312138844a19","as":"/questions-and-answers/a-ball-is-shot-from-the-ground-into-the-air.-at-a-height-of-9.4-m-its-velocity-is-7.71-6.2-ms-with-i/a34e35eb-50ec-4655-bd04-312138844a19"},"content":"A ball is shot from the ground into the air. At a height of 9.4 m, its velocity is = 7.71+ 6.27 m/s, with i horizontal and upward. (a)\nTo what maximum height does the ball rise? (b) What total horizontal distance does the ball travel? What are the (c) magnitude and (d)\nangle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground?"}},{"type":"QNA","answerText":"The given information in the question is a displacement vector,? = [3.1?2, 2.0? 0]. The displacement vector represents the change in the position of an object with time. The question asks for various quantities related to the position, velocity, and acceleration of the object as a function of time.","questionId":"a39f5961-1d1d-4590-be87-912dc892c8c6","questionText":"Given the displacement vector ? =[3.1?2, 2.0?, 0]:(a) what is the position of the object at time? = 2.1 ? assuming the object started at theorigin?(b) what is the distance the object has traveled at? = 2.1 ??(c) what is the velocity of the object as a functionof time?(d) what is the velocity of the object at ? = 0, ? =2.1 ? and ? = 4.2 ??(e) what is the speed of the object at the timesgiven in part (d). Are the speed evenly spaced?Would you expect this? Why or why not?(f) what is the acceleration of the object at? = 0, ? = 2.1 ? and ? = 4.2 ??","slug":"given-the-displacement-vector-3.12-2.0-0-a-what-is-the-position-of-the-object-at-time-2.1-assuming-t","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=a39f5961-1d1d-4590-be87-912dc892c8c6","as":"/questions-and-answers/given-the-displacement-vector-3.12-2.0-0-a-what-is-the-position-of-the-object-at-time-2.1-assuming-t/a39f5961-1d1d-4590-be87-912dc892c8c6"},"content":"Given the displacement vector ? =[3.1?2, 2.0?, 0]:(a) what is the position of the object at time? = 2.1 ? assuming the object started at theorigin?(b) what is the distance the object has traveled at? = 2.1 ??(c) what is the velocity of the object as a functionof time?(d) what is the velocity of the object at ? = 0, ? =2.1 ? and ? = 4.2 ??(e) what is the speed of the object at the timesgiven in part (d). Are the speed evenly spaced?Would you expect this? Why or why not?(f) what is the acceleration of the object at? = 0, ? = 2.1 ? and ? = 4.2 ??"}},{"type":"QNA","answerText":"The horizontal component of velocity do no change throughout the trajectories path.\nThe horizontal component of velocity is\nvx=v0cosθ=25.0 mscos35°=20.48 ms","questionId":"b3ec2cff-4a47-466b-8269-4ce5f76a44aa","questionText":"At t = 0, a stone is thrown at an angle of 35.0 ◦ above the horizontal with an initial speed equal to 25.0 ms−1. Calculate the magnitudes of the horizontal and vertical components of its displacement at t = 1.20 s.","slug":"at-t-0-a-stone-is-thrown-at-an-angle-of-35.0-above-the-horizontal-with-an-initial-speed-equal-to-25.","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=b3ec2cff-4a47-466b-8269-4ce5f76a44aa","as":"/questions-and-answers/at-t-0-a-stone-is-thrown-at-an-angle-of-35.0-above-the-horizontal-with-an-initial-speed-equal-to-25./b3ec2cff-4a47-466b-8269-4ce5f76a44aa"},"content":"At t = 0, a stone is thrown at an angle of 35.0 ◦ above the horizontal with an initial speed equal to 25.0 ms−1. Calculate the magnitudes of the horizontal and vertical components of its displacement at t = 1.20 s."}},{"type":"QNA","answerText":"","questionId":"b520393e-1c6e-4440-a315-e480ffe2ead2","questionText":"A plane flies 493 km east from city A to city B in 45.0 min and then 983 km south from city B to city C in 1.30 h. For the total\ntrip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its\naverage velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180\ndegrees, measured from the +x direction (east).\n(a) Number\ni\nUnits\n(b) Number\nUnits\n(c) Number\ni\nUnits\n(d) Number\ni\nUnits\n(e) Number\nUnits\nII","slug":"a-plane-flies-493-km-east-from-city-a-to-city-b-in-45.0-min-and-then-983-km-south-from-city-b-to-cit","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=b520393e-1c6e-4440-a315-e480ffe2ead2","as":"/questions-and-answers/a-plane-flies-493-km-east-from-city-a-to-city-b-in-45.0-min-and-then-983-km-south-from-city-b-to-cit/b520393e-1c6e-4440-a315-e480ffe2ead2"},"content":"A plane flies 493 km east from city A to city B in 45.0 min and then 983 km south from city B to city C in 1.30 h. For the total\ntrip, what are the (a) magnitude and (b) direction of the plane's displacement, the (c) magnitude and (d) direction of its\naverage velocity, and (e) its average speed? Give your angles as positive or negative values of magnitude less than 180\ndegrees, measured from the +x direction (east).\n(a) Number\ni\nUnits\n(b) Number\nUnits\n(c) Number\ni\nUnits\n(d) Number\ni\nUnits\n(e) Number\nUnits\nII"}},{"type":"QNA","answerText":"","questionId":"b784c9f7-c84b-47ce-b0e3-6a1fcc40b201","questionText":"Please asap","slug":"a-particle-travels-along-the-following-vectors-in-succession-d1-5i-d2-12j-and-d3-2i-4j-and-d4-6i-5j.","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=b784c9f7-c84b-47ce-b0e3-6a1fcc40b201","as":"/questions-and-answers/a-particle-travels-along-the-following-vectors-in-succession-d1-5i-d2-12j-and-d3-2i-4j-and-d4-6i-5j./b784c9f7-c84b-47ce-b0e3-6a1fcc40b201"},"content":"Please asap"}},{"type":"QNA","answerText":"Given:\nInitial velocity,v→=3i^m/sAcceleration, a→=-1i^-0.5j^m/s2\nThe three Newton's laws of motion are classical mechanics laws that define the connection between an object's motion and the forces acting on it. These statutes can be summarized as follows:\nLaw 1: Unless acted upon by a force, a body remains in its condition of rest or uniform motion along a straight line.\nLaw 2: A body operated upon by a force moves in such a way that the force matches the time rate of change of momentum.\nLaw 3: When two bodies exert forces on one other, the magnitude and direction of the forces are identical.","questionId":"ce370336-73fa-495d-8095-1097c9f0248c","questionText":"A particle leaves the origin with an initial velocity\n3.00î m/s and a constant acceleration ở\n-1.00î – 0.50ĵ m/s². When it reaches its maximum x\ncoordinate, what are its (a) velocity and (b) position\nvector?","slug":"a-particle-leaves-the-origin-with-an-initial-velocity-3.00i-ms-and-a-constant-acceleration-a-1.00i-0","childSubject":{"title":"Advanced Physics","shortName":"advanced-physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=ce370336-73fa-495d-8095-1097c9f0248c","as":"/questions-and-answers/a-particle-leaves-the-origin-with-an-initial-velocity-3.00i-ms-and-a-constant-acceleration-a-1.00i-0/ce370336-73fa-495d-8095-1097c9f0248c"},"content":"A particle leaves the origin with an initial velocity\n3.00î m/s and a constant acceleration ở\n-1.00î – 0.50ĵ m/s². When it reaches its maximum x\ncoordinate, what are its (a) velocity and (b) position\nvector?"}},{"type":"QNA","answerText":"","questionId":"cec75a84-284b-4d17-8012-6d7f9802d493","questionText":"A proton initially has 7 = (-7.10)î + (5.10)Ƒ + (−6.60)î\n:\nand then 2.70 s later has 7 = (4.70)î + (5.10)ĵ + (13.0)ê (in\navg\nmeters per second). (a) For that 2.70 s, what is the proton's average acceleration a in unit vector notation, (b) in magnitude, and\nthe angle between a and the positive direction of the x axis?\navg\n(a) Number i 11.8\n(b) Number i\n(c) Number\ni\nî+\nUnits\nUnits\ni\n19.6\nk Units\nm/s","slug":"a-proton-initially-has-7.10i-5.10-6.60-a.-6.60-and-then-2.70-s-later-has-7-4.70-5.10-13.0-i-meters-p","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=cec75a84-284b-4d17-8012-6d7f9802d493","as":"/questions-and-answers/a-proton-initially-has-7.10i-5.10-6.60-a.-6.60-and-then-2.70-s-later-has-7-4.70-5.10-13.0-i-meters-p/cec75a84-284b-4d17-8012-6d7f9802d493"},"content":"A proton initially has 7 = (-7.10)î + (5.10)Ƒ + (−6.60)î\n:\nand then 2.70 s later has 7 = (4.70)î + (5.10)ĵ + (13.0)ê (in\navg\nmeters per second). (a) For that 2.70 s, what is the proton's average acceleration a in unit vector notation, (b) in magnitude, and\nthe angle between a and the positive direction of the x axis?\navg\n(a) Number i 11.8\n(b) Number i\n(c) Number\ni\nî+\nUnits\nUnits\ni\n19.6\nk Units\nm/s"}},{"type":"QNA","answerText":"Write down the given values using suitable variables.\n\nHere r signifies initial position vector, u signifies initial velocity vector, a signifies acceleration vector, and t signifies time.","questionId":"d6391a6c-1fbc-4540-8d6f-49dc7b64ec89","questionText":"A snowmobile is originally at the point with position vector 30.5 m at 95.0° counterclockwise from the x-axis, moving with velocity 4.89 m/s at 40.0°. It moves with a constant acceleration 1.72 m/s2 at 200°. After 5.00 s have elapsed, find the following. (Express your answers in vector form.)\n(a) its velocity vector.\n \n(b) its position vector.","slug":"a-snowmobile-is-originally-at-the-point-with-position-vector30.5m-at-95.0counterclockwise-from-the-x","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=d6391a6c-1fbc-4540-8d6f-49dc7b64ec89","as":"/questions-and-answers/a-snowmobile-is-originally-at-the-point-with-position-vector30.5m-at-95.0counterclockwise-from-the-x/d6391a6c-1fbc-4540-8d6f-49dc7b64ec89"},"content":"A snowmobile is originally at the point with position vector 30.5 m at 95.0° counterclockwise from the x-axis, moving with velocity 4.89 m/s at 40.0°. It moves with a constant acceleration 1.72 m/s2 at 200°. After 5.00 s have elapsed, find the following. (Express your answers in vector form.)\n(a) its velocity vector.\n \n(b) its position vector."}},{"type":"QNA","answerText":"","questionId":"d9dc340a-ede5-408b-af1f-56e068e93048","questionText":"Number\nAn ion's position vector is initially\n7 = (2.4 m )î + (−7.4 m )3 + (6.5 m ). In unit-vector notation, what is its average velocity during the 6.7 s?\n)ĵ\ni 1\n+\n=\n9.1 m\n)i + (−9.9 m )ĵ + (−10 m )k,\n) + (-10 m ), and 6.7 s later it is\n-0.37313433\nĴ\n+\nMI\n-2.46268657\nk Units m/s","slug":"an-ions-position-vector-is-initially-7-9.1-2.4-m-i-7.4-7-number-i-1-m-i-i-9.9-m-7.4-m-6.5-m-.-in-10-","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=d9dc340a-ede5-408b-af1f-56e068e93048","as":"/questions-and-answers/an-ions-position-vector-is-initially-7-9.1-2.4-m-i-7.4-7-number-i-1-m-i-i-9.9-m-7.4-m-6.5-m-.-in-10-/d9dc340a-ede5-408b-af1f-56e068e93048"},"content":"Number\nAn ion's position vector is initially\n7 = (2.4 m )î + (−7.4 m )3 + (6.5 m ). In unit-vector notation, what is its average velocity during the 6.7 s?\n)ĵ\ni 1\n+\n=\n9.1 m\n)i + (−9.9 m )ĵ + (−10 m )k,\n) + (-10 m ), and 6.7 s later it is\n-0.37313433\nĴ\n+\nMI\n-2.46268657\nk Units m/s"}},{"type":"QNA","answerText":"","questionId":"dcfba911-fc46-4724-868b-9df074dcc135","questionText":"A particle initially located at the origin has an acceleration of a = 2.00ĵ m/s² and an initial velocity of = 6.00î m/s.\n(a) Find the vector position of the particle at any time t (where t is measured in seconds).\n(\ntî +\n(²ĵ) m\nf\n(b) Find the velocity of the particle at any time t.\n(\nî+\ntj) m/s\n(c) Find the coordinates of the particle at t = 7.00 s.\nX =\ny =\nm\nm\n(d) Find the speed of the particle at t = 7.00 s.\nm/s\nSubmit Answer","slug":"a-particle-initially-located-at-the-origin-has-an-acceleration-of-a-2.00-ms-and-an-initial-velocity-","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=dcfba911-fc46-4724-868b-9df074dcc135","as":"/questions-and-answers/a-particle-initially-located-at-the-origin-has-an-acceleration-of-a-2.00-ms-and-an-initial-velocity-/dcfba911-fc46-4724-868b-9df074dcc135"},"content":"A particle initially located at the origin has an acceleration of a = 2.00ĵ m/s² and an initial velocity of = 6.00î m/s.\n(a) Find the vector position of the particle at any time t (where t is measured in seconds).\n(\ntî +\n(²ĵ) m\nf\n(b) Find the velocity of the particle at any time t.\n(\nî+\ntj) m/s\n(c) Find the coordinates of the particle at t = 7.00 s.\nX =\ny =\nm\nm\n(d) Find the speed of the particle at t = 7.00 s.\nm/s\nSubmit Answer"}},{"type":"QNA","answerText":"The velocity vector is calculated by taking the derivative of given position vector r(t).","questionId":"e1beedbe-bec9-4c79-8f94-e2f9864c7b2e","questionText":"Given the position vector ~r(t) = t^2ˆi+tˆj in meters, what is the magnitudeof the velocity vector at a time of three seconds?","slug":"given-the-position-vector-~rt-t2itj-in-meters-what-is-the-magnitude-of-the-velocity-vector-at-a-time","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=e1beedbe-bec9-4c79-8f94-e2f9864c7b2e","as":"/questions-and-answers/given-the-position-vector-~rt-t2itj-in-meters-what-is-the-magnitude-of-the-velocity-vector-at-a-time/e1beedbe-bec9-4c79-8f94-e2f9864c7b2e"},"content":"Given the position vector ~r(t) = t^2ˆi+tˆj in meters, what is the magnitudeof the velocity vector at a time of three seconds?"}},{"type":"QNA","answerText":"","questionId":"e57668a3-c37d-4919-a59f-89d2dd020031","questionText":"A snowmobile is originally at the point with position vector 27.1 m at 95.0° counterclockwise from the x axis, moving with velocity 4.13 m/s at 40.0°. It moves with constant acceleration 15 m at 200 After 5.00 s have elapsed, find the following. (Express your answers in vector form.)\n(a) its velocity vector\n(b) its position vector","slug":"snowmobile-is-originally-at-the-point-with-position-vector-27.1-m-at-95.0-counterclockwise-from-the-","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=e57668a3-c37d-4919-a59f-89d2dd020031","as":"/questions-and-answers/snowmobile-is-originally-at-the-point-with-position-vector-27.1-m-at-95.0-counterclockwise-from-the-/e57668a3-c37d-4919-a59f-89d2dd020031"},"content":"A snowmobile is originally at the point with position vector 27.1 m at 95.0° counterclockwise from the x axis, moving with velocity 4.13 m/s at 40.0°. It moves with constant acceleration 15 m at 200 After 5.00 s have elapsed, find the following. (Express your answers in vector form.)\n(a) its velocity vector\n(b) its position vector"}},{"type":"QNA","answerText":"Given :\nThe ball is thrown at a velocity v = 7.5 i^ + 6.1 j^\nThe ball is thrown at height h= 7.5 m","questionId":"ea7da52d-b952-48c9-8017-8d0c8dface57","questionText":"A ball is shot from the ground into the air. At a height of 7.5 m, its velocity is v = 7.5i + 6.1j m/s, with i horizontal and j upward. (a) To what maximum height does the ball rise? (b) What total horizontal\ndistance does the ball travel? What are the (c) magnitude and (d) angle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground?\n(a) Number\nUnits\n(b) Number\nUnits\n(c) Number\nUnits\n(d) Number\nUnits","slug":"a-ball-is-shot-from-the-ground-into-the-air.-at-a-height-of-7.5-m-its-velocity-is-v-7.5i-6.1j-ms-wit","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=ea7da52d-b952-48c9-8017-8d0c8dface57","as":"/questions-and-answers/a-ball-is-shot-from-the-ground-into-the-air.-at-a-height-of-7.5-m-its-velocity-is-v-7.5i-6.1j-ms-wit/ea7da52d-b952-48c9-8017-8d0c8dface57"},"content":"A ball is shot from the ground into the air. At a height of 7.5 m, its velocity is v = 7.5i + 6.1j m/s, with i horizontal and j upward. (a) To what maximum height does the ball rise? (b) What total horizontal\ndistance does the ball travel? What are the (c) magnitude and (d) angle (below the horizontal; give as negative) of the ball's velocity just before it hits the ground?\n(a) Number\nUnits\n(b) Number\nUnits\n(c) Number\nUnits\n(d) Number\nUnits"}},{"type":"QNA","answerText":"From the question it is given that: \nAcceleration: a(t) = cost i^ + 5sint j^ initial velocity: (uo,vo) = (0,5)Initial position: (xo,yo) = (2,0)","questionId":"eb1a1a7b-d9d7-4d16-8bf6-8a05bb05df08","questionText":"IT.0.0a\nGiven an acceleration vector, initial velocity (uo.Vo), and initial position {xo.yo}, find the velocity and position vectors for t2 0.\na(t) = (cos t,5 sin t. (Uo Vo) = (0,5) , (Xo.Yo) = (2.0)\nWhat is the velc\n| vector?\nv(t) =","slug":"given-an-acceleration-vector-initial-velocity-uo.vo-and-initial-position-xg.yo-find-the-velocity-and","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=eb1a1a7b-d9d7-4d16-8bf6-8a05bb05df08","as":"/questions-and-answers/given-an-acceleration-vector-initial-velocity-uo.vo-and-initial-position-xg.yo-find-the-velocity-and/eb1a1a7b-d9d7-4d16-8bf6-8a05bb05df08"},"content":"IT.0.0a\nGiven an acceleration vector, initial velocity (uo.Vo), and initial position {xo.yo}, find the velocity and position vectors for t2 0.\na(t) = (cos t,5 sin t. (Uo Vo) = (0,5) , (Xo.Yo) = (2.0)\nWhat is the velc\n| vector?\nv(t) ="}},{"type":"QNA","answerText":"The initial velocity of the particle is v→=3.61i^ m/s.\nThe acceleration of the particle is a→=-1.84i^-3.82j^ m/s2.","questionId":"eba530ca-c4cc-4bef-9fb8-4164fa513e73","questionText":"A particle leaves the origin with an initial velocity = (3.61î) m/s and a constant acceleration\nWhen the particle reaches its maximum x coordinate, what are (a) its velocity, (b) its position vector?\n=\n( – 1.84î – 3.827) m/s²","slug":"a-particle-leaves-the-origin-with-an-initial-velocity-v-3.611-ms-and-a-constant-acceleration-a-1.84i","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=eba530ca-c4cc-4bef-9fb8-4164fa513e73","as":"/questions-and-answers/a-particle-leaves-the-origin-with-an-initial-velocity-v-3.611-ms-and-a-constant-acceleration-a-1.84i/eba530ca-c4cc-4bef-9fb8-4164fa513e73"},"content":"A particle leaves the origin with an initial velocity = (3.61î) m/s and a constant acceleration\nWhen the particle reaches its maximum x coordinate, what are (a) its velocity, (b) its position vector?\n=\n( – 1.84î – 3.827) m/s²"}},{"type":"QNA","answerText":"The initial position of the rabbit, r1,x = -10.3 m and r1,y = 23.1 mThe average velocity of the rabbit, vav, x = -2.17 m/s and vav,y = 1.05 m/sThe time interval, t = 12.7 s","questionId":"edcdec0d-ede6-4191-84bb-f03d30ac10ad","questionText":"Answer the question correctly. Thank you!!","slug":"starting-from-a-location-with-position-vector-1x-10.3-m-and-ry-23.1-m-a-rabbit-hops-around-for-12.7-","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=edcdec0d-ede6-4191-84bb-f03d30ac10ad","as":"/questions-and-answers/starting-from-a-location-with-position-vector-1x-10.3-m-and-ry-23.1-m-a-rabbit-hops-around-for-12.7-/edcdec0d-ede6-4191-84bb-f03d30ac10ad"},"content":"Answer the question correctly. Thank you!!"}},{"type":"QNA","answerText":"Position vector is given by,\nr→(t)=x(t)i+y(t)j\nNow,\nx(t)=a(t)+b\nSubstitute the value of a and b in above equation,\nx(t)=1(t)+1..........(1)\n \ny(t)=ct2+d\nSubstitute the value of c and d in above equationy(t)=0.125(t2)+1.......(2),","questionId":"eecb70b0-061d-4043-ad68-39bd63d33dd2","questionText":"Do the first question","slug":"1.-suppose-the-position-vector-for-a-particle-is-given-as-a-func-tion-of-time-by-f-x1i-y1j-with-x1-y","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=eecb70b0-061d-4043-ad68-39bd63d33dd2","as":"/questions-and-answers/1.-suppose-the-position-vector-for-a-particle-is-given-as-a-func-tion-of-time-by-f-x1i-y1j-with-x1-y/eecb70b0-061d-4043-ad68-39bd63d33dd2"},"content":"Do the first question"}},{"type":"QNA","answerText":"","questionId":"ef2d6132-5f66-4632-bad8-914d22011f63","questionText":"At time t = 0, a projectile is launched from ground level. At t = 2.00 s, it is displacedd = 47 m horizontally and h = 77 m vertically above\nthe launch point. What are the (a) horizontal and (b)\nvertical components of the initial velocity of the projectile? (c) At the instant it reaches its maximum height above ground level, what is\nits horizontal displacement D from the launch point?\n(a) Number\ni\nUnit\n(b) Number\nUnit\n(c) Number\ni\nUnit\n\u003e","slug":"at-time-t-0-a-projectile-is-launched-from-ground-level.-at-t-2.00-s-it-is-displaced-d-47-m-horizonta","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=ef2d6132-5f66-4632-bad8-914d22011f63","as":"/questions-and-answers/at-time-t-0-a-projectile-is-launched-from-ground-level.-at-t-2.00-s-it-is-displaced-d-47-m-horizonta/ef2d6132-5f66-4632-bad8-914d22011f63"},"content":"At time t = 0, a projectile is launched from ground level. At t = 2.00 s, it is displacedd = 47 m horizontally and h = 77 m vertically above\nthe launch point. What are the (a) horizontal and (b)\nvertical components of the initial velocity of the projectile? (c) At the instant it reaches its maximum height above ground level, what is\nits horizontal displacement D from the launch point?\n(a) Number\ni\nUnit\n(b) Number\nUnit\n(c) Number\ni\nUnit\n\u003e"}},{"type":"QNA","answerText":"","questionId":"f2d64d28-1c34-4679-ace4-e71e5dfde30d","questionText":"A particle located initially at (1.5ˆj + 4.0ˆk) m undergoes a displacement of (2.5ˆi+ 3.2ˆj − 1.2ˆk) m. (a) What is the final position of the particle? (b) If the time needed to displace the particle from its initial position to its final position is 5 s, determine the particle’s average velocity vector.","slug":"a-particle-located-initially-at-1.5j-4.0k-m-undergoes-a-displacement-of-2.5i-3.2j-1.2k-m.-a-what-is-","childSubject":{"title":"Physics","shortName":"physics"},"parentSubject":{"title":"Science","shortName":"science"},"computed":{"hrefAndAs":{"href":"/my-questions?questionId=f2d64d28-1c34-4679-ace4-e71e5dfde30d","as":"/questions-and-answers/a-particle-located-initially-at-1.5j-4.0k-m-undergoes-a-displacement-of-2.5i-3.2j-1.2k-m.-a-what-is-/f2d64d28-1c34-4679-ace4-e71e5dfde30d"},"content":"A particle located initially at (1.5ˆj + 4.0ˆk) m undergoes a displacement of (2.5ˆi+ 3.2ˆj − 1.2ˆk) m. (a) What is the final position of the particle? (b) If the time needed to displace the particle from its initial position to its final position is 5 s, determine the particle’s average velocity vector."}}],"popularTextbooks":[{"bookId":"c0e7bc4d-3f7d-11e8-a3e8-a45d36699311","studyGuideAvailable":true,"isbn13":"9781305952300","bookTitle":"College Physics","edition":"11","author":"Raymond A. Serway, Chris Vuille","publisher":"Cengage Learning","isHighSchool":false,"smallImage":"https://www.bartleby.com/isbn_cover_images/9781305952300/9781305952300_smallCoverImage.gif","slug":"college-physics-11th-edition","isFree":false,"textBookUrl":"https://amzn.to/4791Ipj","solution":{"text":"Length is the measurement of distance between the two ends of an object. 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