The figure above gives an overhead view of the path taken by a cue ball with mass m as it bounces from a rail of a pool table. The ball's initial speed is v; and the angle of impact is 01. The bounce reverses the y component of the ball's velocity but does not alter the x component. NOTE: Express your answers in terms of the given variables (m, v;, 0 1).Enclose arguments of functions in parentheses. For example, sin(2x). (a) What is 02? 02 T – 01 -
The figure above gives an overhead view of the path taken by a cue ball with mass m as it bounces from a rail of a pool table. The ball's initial speed is v; and the angle of impact is 01. The bounce reverses the y component of the ball's velocity but does not alter the x component. NOTE: Express your answers in terms of the given variables (m, v;, 0 1).Enclose arguments of functions in parentheses. For example, sin(2x). (a) What is 02? 02 T – 01 -
College Physics
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Author:Raymond A. Serway, Chris Vuille
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Chapter1: Units, Trigonometry. And Vectors
Section: Chapter Questions
Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...
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![The figure above illustrates an overhead view of the path taken by a cue ball with mass \( m \) as it bounces off a rail of a pool table. The ball's initial speed is \( v_i \) and the angle of impact is \( \theta_1 \). The bounce reverses the \( y \)-component of the ball’s velocity but does not alter the \( x \)-component.
**Note:** Express your answers in terms of the given variables (\( m, v_i, \theta_1 \)). Enclose arguments of functions in parentheses. For example, \(\sin(2x)\).
**(a) What is \( \theta_2 \)?**
\[
\theta_2 = \pi - \theta_1 \quad \textcolor{red}{\text{✘ Incorrect}}
\]
**(b) What is the change in the ball’s linear momentum in unit-vector notation?** (The fact that the ball rolls is irrelevant to the problem.)
\[
\Delta \vec{p} = 0 \, \hat{\imath} + (-2 m v_i \cos(\theta_1)) \, \hat{\jmath} \quad \textcolor{green}{\text{✔ Correct}}
\]
**Explanation:**
- **Diagram:** It shows a cue ball approaching a rail at an angle \( \theta_1 \) and bouncing off at an angle \( \theta_2 \), with the direction labeled along the \( x \)-axis.
- The angle \( \theta_2 \) should be calculated correctly by considering the properties of the bounce and symmetry.
- The change in momentum tensor indicates that the \( x \)-component remains constant, whereas the \( y \)-component reverses, hence the negative sign in the momentum expression.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82e82db8-362b-4865-93d3-f20edd638ab0%2F5da1c4fa-dec5-4c3e-975f-aefaeff7ea77%2Fnkunlj8_processed.png&w=3840&q=75)
Transcribed Image Text:The figure above illustrates an overhead view of the path taken by a cue ball with mass \( m \) as it bounces off a rail of a pool table. The ball's initial speed is \( v_i \) and the angle of impact is \( \theta_1 \). The bounce reverses the \( y \)-component of the ball’s velocity but does not alter the \( x \)-component.
**Note:** Express your answers in terms of the given variables (\( m, v_i, \theta_1 \)). Enclose arguments of functions in parentheses. For example, \(\sin(2x)\).
**(a) What is \( \theta_2 \)?**
\[
\theta_2 = \pi - \theta_1 \quad \textcolor{red}{\text{✘ Incorrect}}
\]
**(b) What is the change in the ball’s linear momentum in unit-vector notation?** (The fact that the ball rolls is irrelevant to the problem.)
\[
\Delta \vec{p} = 0 \, \hat{\imath} + (-2 m v_i \cos(\theta_1)) \, \hat{\jmath} \quad \textcolor{green}{\text{✔ Correct}}
\]
**Explanation:**
- **Diagram:** It shows a cue ball approaching a rail at an angle \( \theta_1 \) and bouncing off at an angle \( \theta_2 \), with the direction labeled along the \( x \)-axis.
- The angle \( \theta_2 \) should be calculated correctly by considering the properties of the bounce and symmetry.
- The change in momentum tensor indicates that the \( x \)-component remains constant, whereas the \( y \)-component reverses, hence the negative sign in the momentum expression.
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