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<h2 class="hd hd-2 unit-title">Topics and Reading List</h2>
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<p>Now that we have introduced position, velocity, and acceleration in the simple case of one dimension, we will generalize these concepts to two dimensions. </p><p> As you go through the lesson, you will find this list of reading from the textbook complementary to the videos and exercises, and on many occasions will contain relevant material to the presentation:</p><ul><li> Vector Description of Motion in 2D: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/5/2"><i class="it">chapter 5, section 1</i></a></li><li> Projectile Motion: <a href="/courses/course-v1:MITx+8.01.1x+3T2018/pdfbook/0/chapter/5/3"><i class="it">chapter 5, section 2</i></a></li></ul>
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<h2 class="hd hd-2 unit-title">L3v1: Coordinate System and Position Vector in 2D</h2>
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<h3 class="hd hd-2">L3v1: Coordinate System and Position Vector in 2D</h3>
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<h2 class="hd hd-2 unit-title">L3Q1: Position, Displacement and Distance in 2D</h2>
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L3Q1-1: Position Vector in 2D
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<p>
Consider two coordinate systems: 1 and 2. Coordinate system 1 is the one with the axes shown in solid lines, coordinate system 2 is the one with the axes shown as dashed lines. The origins of the coordinate systems are marked as [mathjaxinline]O_1[/mathjaxinline] and [mathjaxinline]O_2[/mathjaxinline], respectively. The scale on all axes is the same, 1 m. A particle is moving from an initial position, point [mathjaxinline]A[/mathjaxinline], to a final position, point [mathjaxinline]B[/mathjaxinline]. All numbers marked in the diagram represent the coordinate of the corresponding points in coordinate system 1. The unit vectors of coordinate system 1 are [mathjaxinline]\hat{i}_1[/mathjaxinline] and [mathjaxinline]\hat{j}_1[/mathjaxinline], and the unit vectors of coordinate system 2 are [mathjaxinline]\hat{i}_2[/mathjaxinline] and [mathjaxinline]\hat{j}_2[/mathjaxinline]. </p>
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<img src="/assets/courseware/v1/8ea08fe296637084b601e71cf4f0ecdc/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_ls01_07.svg" width="440"/>
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<p><b class="bfseries">(Part a)</b> What is the correct notation for vector [mathjaxinline]\vec{r}_{A1}[/mathjaxinline], the initial position of the particle in coordinate system 1? Express your answers in terms of the the unit vectors of coordinate system 1. Enter hati_1 for [mathjaxinline]\hat{i}_1[/mathjaxinline] and hatj_1 for [mathjaxinline]\hat{j}_1[/mathjaxinline] </p>
<p><p style="display:inline">[mathjaxinline]\vec{r}_{A1} =[/mathjaxinline] </p><div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ls_ls01_ls01_07_2_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_ls_ls01_ls01_07_2_1" id="input_ls_ls01_ls01_07_2_1" aria-describedby="trailing_text_ls_ls01_ls01_07_2_1 status_ls_ls01_ls01_07_2_1" value="" class="math" size="25"/>
<span class="trailing_text" id="trailing_text_ls_ls01_ls01_07_2_1">[mathjaxinline]\mathrm{m}[/mathjaxinline]</span>
<span class="status unanswered" id="status_ls_ls01_ls01_07_2_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<div id="display_ls_ls01_ls01_07_2_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ls_ls01_ls01_07_2_1_dynamath" name="input_ls_ls01_ls01_07_2_1_dynamath"/>
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</div></div><div class="solution-span">
<span id="solution_ls_ls01_ls01_07_solution_1"/>
</div><b class="bfseries">(Part b)</b> What is the correct notation for [mathjaxinline]\vec{r}_{A2}[/mathjaxinline], the initial position of the particle in coordinate system 2? Express your answers in terms of the the unit vectors of coordinate system 2. Enter hati_2 for [mathjaxinline]\hat{i}_2[/mathjaxinline] and hatj_2 for [mathjaxinline]\hat{j}_2[/mathjaxinline] </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{r}_{A2} =[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ls_ls01_ls01_07_3_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_ls_ls01_ls01_07_3_1" id="input_ls_ls01_ls01_07_3_1" aria-describedby="trailing_text_ls_ls01_ls01_07_3_1 status_ls_ls01_ls01_07_3_1" value="" class="math" size="25"/>
<span class="trailing_text" id="trailing_text_ls_ls01_ls01_07_3_1">[mathjaxinline]\mathrm{m}[/mathjaxinline]</span>
<span class="status unanswered" id="status_ls_ls01_ls01_07_3_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<div id="display_ls_ls01_ls01_07_3_1" class="equation">`{::}`</div>
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<span id="solution_ls_ls01_ls01_07_solution_2"/>
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<p><b class="bfseries">(Part c)</b> What is the correct notation for [mathjaxinline]\vec{r}_{B2}[/mathjaxinline], the final position of the particle in coordinate system 2? Express your answers in terms of the unit vectors of coordinate system 2. Enter hati_2 for [mathjaxinline]\hat{i}_2[/mathjaxinline] and hatj_2 for [mathjaxinline]\hat{j}_2[/mathjaxinline] <p style="display:inline">[mathjaxinline]\vec{r}_{B2} =[/mathjaxinline] </p> <div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ls_ls01_ls01_07_4_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_ls_ls01_ls01_07_4_1" id="input_ls_ls01_ls01_07_4_1" aria-describedby="trailing_text_ls_ls01_ls01_07_4_1 status_ls_ls01_ls01_07_4_1" value="" class="math" size="25"/>
<span class="trailing_text" id="trailing_text_ls_ls01_ls01_07_4_1">[mathjaxinline]\mathrm{m}[/mathjaxinline]</span>
<span class="status unanswered" id="status_ls_ls01_ls01_07_4_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<div id="display_ls_ls01_ls01_07_4_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ls_ls01_ls01_07_4_1_dynamath" name="input_ls_ls01_ls01_07_4_1_dynamath"/>
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</div></div> </p>
<p>
<div class="solution-span">
<span id="solution_ls_ls01_ls01_07_solution_3"/>
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<p><b class="bfseries">(Part d)</b> What is [mathjaxinline]\vec{r}_{B1}-\vec{r}_{A1}[/mathjaxinline], the displacement vector between the final and the initial positions in coordinate system 1? Express your answers in terms of the unit vectors of coordinate system 1. Enter hati_1 for [mathjaxinline]\hat{i}_1[/mathjaxinline] and hatj_1 for [mathjaxinline]\hat{j}_1[/mathjaxinline] </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{r}_{B1}-\vec{r}_{A1} =[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 4" role="group"><div id="inputtype_ls_ls01_ls01_07_5_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_ls_ls01_ls01_07_5_1" id="input_ls_ls01_ls01_07_5_1" aria-describedby="trailing_text_ls_ls01_ls01_07_5_1 status_ls_ls01_ls01_07_5_1" value="" class="math" size="25"/>
<span class="trailing_text" id="trailing_text_ls_ls01_ls01_07_5_1">[mathjaxinline]\mathrm{m}[/mathjaxinline]</span>
<span class="status unanswered" id="status_ls_ls01_ls01_07_5_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
<p id="answer_ls_ls01_ls01_07_5_1" class="answer"/>
<div id="display_ls_ls01_ls01_07_5_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ls_ls01_ls01_07_5_1_dynamath" name="input_ls_ls01_ls01_07_5_1_dynamath"/>
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</div></div>
</p>
<p>
<div class="solution-span">
<span id="solution_ls_ls01_ls01_07_solution_4"/>
</div></p>
<p><b class="bfseries">(Part e)</b> What is [mathjaxinline]\vec{r}_{B2}-\vec{r}_{A2}[/mathjaxinline], the displacement vector between the final and the initial positions in coordinate system 2? Express your answers in terms of the unit vectors of coordinate system 2. Enter hati_2 for [mathjaxinline]\hat{i}_2[/mathjaxinline] and hatj_2 for [mathjaxinline]\hat{j}_2[/mathjaxinline] </p>
<p>
<p style="display:inline">[mathjaxinline]\vec{r}_{B2}-\vec{r}_{A2} =[/mathjaxinline] </p>
<div class="inline" tabindex="-1" aria-label="Question 5" role="group"><div id="inputtype_ls_ls01_ls01_07_6_1" class="text-input-dynamath capa_inputtype inline textline">
<div class="unanswered inline">
<input type="text" name="input_ls_ls01_ls01_07_6_1" id="input_ls_ls01_ls01_07_6_1" aria-describedby="trailing_text_ls_ls01_ls01_07_6_1 status_ls_ls01_ls01_07_6_1" value="" class="math" size="25"/>
<span class="trailing_text" id="trailing_text_ls_ls01_ls01_07_6_1">[mathjaxinline]\mathrm{m}[/mathjaxinline]</span>
<span class="status unanswered" id="status_ls_ls01_ls01_07_6_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
</span>
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<div id="display_ls_ls01_ls01_07_6_1" class="equation">`{::}`</div>
<textarea style="display:none" id="input_ls_ls01_ls01_07_6_1_dynamath" name="input_ls_ls01_ls01_07_6_1_dynamath"/>
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<span id="solution_ls_ls01_ls01_07_solution_5"/>
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L3Q1-2: Displacement vs. Distance in 2D
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Mr. Ant is walking around on a grid-marked table. He starts at the origin at [mathjaxinline]t=0[/mathjaxinline] s and follows the green path, reaching the marked points at the indicated times. The grid is in centimeters. </p>
<p>
Answer the questions below aobut Mr. Ant's travels. If the answer is a number, enter a number. If the answer is a vector, enter it in component form. For example, you could enter [mathjaxinline]2\hat{i}+2\hat{j}[/mathjaxinline]. </p>
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<p><b class="bfseries">(Part a)</b> What is the total distance travelled by Mr. Ant? </p>
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<p><b class="bfseries">(Part b)</b> What is Mr. Ant's final displacement from where he started? Express your answers in terms of the cartesian unit vectors. Enter hati for [mathjaxinline]\hat{i}[/mathjaxinline] and hatj for [mathjaxinline]\hat{j}[/mathjaxinline] </p>
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<p><b class="bfseries">(Part c)</b> What is the distance travelled by Mr. Ant between 3 s and 20 s? </p>
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<p><b class="bfseries">(Part d)</b> What is Mr. Ant's displacement from 3 s to 20 s? </p>
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Express your answers in terms of the cartesian unit vectors. Enter hati for [mathjaxinline]\hat{i}[/mathjaxinline] and hatj for [mathjaxinline]\hat{j}[/mathjaxinline] </p>
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<h2 class="hd hd-2 unit-title">L3v2: Instantaneous Velocity in 2D</h2>
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<h2 class="hd hd-2 unit-title">L3Q2: Average velocity vs. Average Speed in 2D</h2>
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L3Q2: Average velocity vs. Average speed in 2D
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Mr. Ant is walking around on a grid-marked table. He starts at the origin at [mathjaxinline]t=0[/mathjaxinline] s and follows the green path, reaching the marked points at the indicated times. The grid is in centimeters. </p>
<p>
Answer the questions below about Mr. Ant's travels. </p>
<center>
<img src="/assets/courseware/v1/b113389668c05c83faf826dd564cc823/asset-v1:MITx+8.01.1x+3T2018+type@asset+block/images_ant_with_grid.svg" width="330"/>
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<p><b class="bfseries">(Part a)</b> What Mr. Ant's average speed for the whole trip? Enter your numerical answer to 2 significant figures. </p>
<p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls01_09_2_1">[mathjaxinline]\mathrm{cm/s}[/mathjaxinline]</span>
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<p><b class="bfseries">(Part b)</b> What is [mathjaxinline]\vec{v}_{avg}[/mathjaxinline], Mr. Ant's average velocity for the whole trip? Enter your numerical answer to 2 significant figures. </p>
<p>
<p style="display:inline">The x-component [mathjaxinline]v_{avg,x}=[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 2" role="group"><div id="inputtype_ls_ls01_ls01_09_3_1" class=" capa_inputtype inline textline">
<div class="unanswered inline">
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<span class="trailing_text" id="trailing_text_ls_ls01_ls01_09_3_1">[mathjaxinline]\mathrm{cm/s}[/mathjaxinline]</span>
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<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<p style="display:inline">The y-component [mathjaxinline]v_{avg,y}=[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ls_ls01_ls01_09_4_1" class=" capa_inputtype inline textline">
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<span class="trailing_text" id="trailing_text_ls_ls01_ls01_09_4_1">[mathjaxinline]\mathrm{cm/s}[/mathjaxinline]</span>
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<p><b class="bfseries">(Part c)</b> What is Mr. Ant's average speed between 3 s and 20 s? Enter your numerical answer to 2 significant figures. </p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls01_09_5_1">[mathjaxinline]\mathrm{cm/s}[/mathjaxinline]</span>
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<p><b class="bfseries">(Part d)</b> What is [mathjaxinline]\vec{v}_{avg}[/mathjaxinline], Mr. Ant's average velocity from 3 s to 20 s? Enter your numerical answer to 2 significant figures. </p>
<p>
<p style="display:inline">The x-component [mathjaxinline]v_{avg,x}=[/mathjaxinline]</p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls01_09_6_1">[mathjaxinline]\mathrm{cm/s}[/mathjaxinline]</span>
<span class="status unanswered" id="status_ls_ls01_ls01_09_6_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<p id="answer_ls_ls01_ls01_09_6_1" class="answer"/>
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</div></div>
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<p>
<p style="display:inline">The y-component [mathjaxinline]v_{avg,y}=[/mathjaxinline]</p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls01_09_7_1">[mathjaxinline]\mathrm{cm/s}[/mathjaxinline]</span>
<span class="status unanswered" id="status_ls_ls01_ls01_09_7_1" data-tooltip="Not yet answered.">
<span class="sr">unanswered</span><span class="status-icon" aria-hidden="true"/>
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<h2 class="hd hd-2 unit-title">L3v3: Instantaneous Acceleration in 2D</h2>
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<h2 class="hd hd-2 unit-title">L3Q3: Position, velocity and acceleration in 2D</h2>
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L3Q3: Position, velocity and acceleration in 2D
</h3>
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<span>
<p>
A particle is moving in the x-y plane. Its position vector, [mathjaxinline]\vec{r}[/mathjaxinline], is given by </p>
<p>
[mathjaxinline]\vec{r}(t) = (6+2t^3) \hat{i} + (3+4t-6t^2) \hat{j}[/mathjaxinline] </p>
<p>
Distances are in meters, and the time, [mathjaxinline]t[/mathjaxinline], is in seconds. </p>
<p><b class="bfseries">(Part a)</b> What are the components of the velocity vector [mathjaxinline]\vec{v}[/mathjaxinline] at [mathjaxinline]t = + 3[/mathjaxinline] s? </p>
<p>
<p style="display:inline">[mathjaxinline]v_ x=[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ls_ls01_ls1_02_2_1" class=" capa_inputtype inline textline">
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<span class="trailing_text" id="trailing_text_ls_ls01_ls1_02_2_1">[mathjaxinline]\mathrm{m\cdot s^{-1}}[/mathjaxinline]</span>
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<p style="display:inline">[mathjaxinline]v_ y=[/mathjaxinline]</p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls1_02_3_1">[mathjaxinline]\mathrm{m\cdot s^{-1}}[/mathjaxinline]</span>
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<p><b class="bfseries">(Part b)</b> What is the speed at [mathjaxinline]t = + 3[/mathjaxinline]s? </p>
<p>
<p style="display:inline">[mathjaxinline]|\vec{v}|=[/mathjaxinline]</p>
<div class="inline" tabindex="-1" aria-label="Question 3" role="group"><div id="inputtype_ls_ls01_ls1_02_4_1" class=" capa_inputtype inline textline">
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<span class="trailing_text" id="trailing_text_ls_ls01_ls1_02_4_1">[mathjaxinline]\mathrm{m\cdot s^{-1}}[/mathjaxinline]</span>
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<p><b class="bfseries">(Part c)</b> What are the components of the acceleration vector [mathjaxinline]\vec{a}[/mathjaxinline] at [mathjaxinline]t = +3[/mathjaxinline] s? </p>
<p>
<p style="display:inline">[mathjaxinline]a_ x=[/mathjaxinline]</p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls1_02_5_1">[mathjaxinline]\mathrm{m\cdot s^{-2}}[/mathjaxinline]</span>
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<p style="display:inline">[mathjaxinline]a_ y=[/mathjaxinline]</p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls1_02_6_1">[mathjaxinline]\mathrm{m\cdot s^{-2}}[/mathjaxinline]</span>
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<p><b class="bfseries">(Part d)</b> What is the magnitude of the acceleration at [mathjaxinline]t = +3[/mathjaxinline] s? </p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls1_02_7_1">[mathjaxinline]\mathrm{m\cdot s^{-2}}[/mathjaxinline]</span>
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<h2 class="hd hd-2 unit-title">L3v4: Projectile Motion</h2>
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<p> A special case of Two Dimensional Motion is the motion of an object with an initial velocity with a non-zero horizontal component under the influence of only the gravitational force. This motion is referred to as Projectile Motion.</p>
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<h3 class="hd hd-2">L3v4: Projectile Motion</h3>
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<h2 class="hd hd-2 unit-title">Demos for Projectile Motion</h2>
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data-metadata='{"end": 0.0, "speed": null, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo01_shooting_apple/handler/transcript/available_translations", "saveStateUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo01_shooting_apple/handler/xmodule_handler/save_user_state", "poster": null, "saveStateEnabled": false, "completionPercentage": 0.95, "captionDataDir": null, "lmsRootURL": "https://openlearninglibrary.mit.edu", "sources": [], "ytApiUrl": "https://www.youtube.com/iframe_api", "ytMetadataEndpoint": "", "transcriptLanguage": "en", "transcriptLanguages": {"en": "English"}, "prioritizeHls": false, "autohideHtml5": false, "recordedYoutubeIsAvailable": true, "generalSpeed": 1.0, "autoAdvance": false, "ytTestTimeout": 1500, "streams": "1.00:KuCAh_s_hFY", "autoplay": false, "publishCompletionUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo01_shooting_apple/handler/publish_completion", "showCaptions": "true", "completionEnabled": false, "savedVideoPosition": 0.0, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo01_shooting_apple/handler/transcript/translation/__lang__", "start": 0.0, "duration": null}'
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<h3 class="hd hd-2">Demo: Relative Motion Gun</h3>
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id="video_demo02_relative_motion"
class="video closed"
data-metadata='{"end": 0.0, "speed": null, "transcriptAvailableTranslationsUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo02_relative_motion/handler/transcript/available_translations", "saveStateUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo02_relative_motion/handler/xmodule_handler/save_user_state", "poster": null, "saveStateEnabled": false, "completionPercentage": 0.95, "captionDataDir": null, "lmsRootURL": "https://openlearninglibrary.mit.edu", "sources": [], "ytApiUrl": "https://www.youtube.com/iframe_api", "ytMetadataEndpoint": "", "transcriptLanguage": "en", "transcriptLanguages": {"en": "English"}, "prioritizeHls": false, "autohideHtml5": false, "recordedYoutubeIsAvailable": true, "generalSpeed": 1.0, "autoAdvance": false, "ytTestTimeout": 1500, "streams": "1.00:JCpOFbY93gs", "autoplay": false, "publishCompletionUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo02_relative_motion/handler/publish_completion", "showCaptions": "true", "completionEnabled": false, "savedVideoPosition": 0.0, "transcriptTranslationUrl": "/courses/course-v1:MITx+8.01.1x+3T2018/xblock/block-v1:MITx+8.01.1x+3T2018+type@video+block@demo02_relative_motion/handler/transcript/translation/__lang__", "start": 0.0, "duration": null}'
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<h2 class="hd hd-2 unit-title">L3WE1: Throwing a projectile (Worked Example)</h2>
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<p> This worked example is a typical projectile motion question. There is no solution video associated with it, so you can try it if you're up for the challenge or else just hit "Check" once to be able to then "Show Answer". </p>
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L3WE1-1: Throwing a projectile (Worked Example)
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A person is playing a game that requires throwing an object onto a ledge. The ledge is at a distance [mathjaxinline]d[/mathjaxinline] and at a height [mathjaxinline]d/2[/mathjaxinline] above the release point. You may neglect air resistance. You may use [mathjaxinline]g[/mathjaxinline] for the magnitude of the gravitational acceleration. The goal of this problem is to find [mathjaxinline]v_0[/mathjaxinline], the magnitude of the launching velocity, and [mathjaxinline]\theta _0[/mathjaxinline], the angle that the launching velocity makes with the horizontal, so that the object is exactly at the top of its flight when it reaches the ledge? </p>
<p><b class="bfseries">(Part a)</b> Calculate [mathjaxinline]v_0[/mathjaxinline]. Express your answer for [mathjaxinline]v_0[/mathjaxinline] in terms of the given quantities [mathjaxinline]d[/mathjaxinline] and [mathjaxinline]g[/mathjaxinline] as needed. </p>
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<p style="display:inline">[mathjaxinline]v_0 =[/mathjaxinline]</p>
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<div id="display_ls_ls01_ls01_10a_2_1" class="equation">`{::}`</div>
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<p><b class="bfseries">(Part b)</b> Calculate [mathjaxinline]\theta _0[/mathjaxinline]. Enter your answer in degrees. </p>
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<p style="display:inline">[mathjaxinline]\theta _0 =[/mathjaxinline]</p>
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<span class="trailing_text" id="trailing_text_ls_ls01_ls01_10a_3_1">[mathjaxinline]\mathrm{^ o}[/mathjaxinline]</span>
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L3WE1-2: Throwing a projectile (Worked Example)
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Once the object reaches the ledge it slows down with a constant deceleration and comes to a stop after sliding a distance [mathjaxinline]s[/mathjaxinline]. </p>
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<p><b class="bfseries">(Part c)</b> What is the magnitude of the horizontal component of the acceleration? Express your answer in terms of the given quantities [mathjaxinline]s[/mathjaxinline] , [mathjaxinline]d[/mathjaxinline] , and [mathjaxinline]g[/mathjaxinline]. <p style="display:inline">[mathjaxinline]|a_ x|=[/mathjaxinline]</p> <div class="inline" tabindex="-1" aria-label="Question 1" role="group"><div id="inputtype_ls_ls01_ls01_10b_2_1" class="text-input-dynamath capa_inputtype inline textline">
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