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 vị 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, vị, 0 1).Enclose arguments of functions in parentheses. For example, sin(2x). (a) What is 02? 02 (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.) Ap = +
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 vị 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, vị, 0 1).Enclose arguments of functions in parentheses. For example, sin(2x). (a) What is 02? 02 (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.) Ap = +
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![**Figure Explanation**
The image provides an overhead view of a cue ball's trajectory as it rebounds off the rail of a pool table. It illustrates the angles and directions before and after the ball's impact with the rail.
- **Diagram Description**:
- The pool table is represented with a top-down view.
- A cue ball is shown moving towards and bouncing away from the rail.
- The angle of incidence before impact is labeled as \( \theta_1 \).
- The angle of reflection after impact is labeled as \( \theta_2 \).
- Axes are labeled as \( x \) (horizontal) and \( y \) (vertical).
**Text Transcription**
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 \( v_i \) 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 \( \theta_2 \)?
\[ \theta_2 = \text{\underline{\hspace{2cm}}} \]
(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.)
\[ \Delta \vec{p} = \text{\underline{\hspace{2cm}}} \, \hat{\imath} + \text{\underline{\hspace{2cm}}} \, \hat{\jmath} \]](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F82e82db8-362b-4865-93d3-f20edd638ab0%2F6c61dd53-0050-4d73-b84d-b5d4cf7c6472%2Fketpczw_processed.png&w=3840&q=75)
Transcribed Image Text:**Figure Explanation**
The image provides an overhead view of a cue ball's trajectory as it rebounds off the rail of a pool table. It illustrates the angles and directions before and after the ball's impact with the rail.
- **Diagram Description**:
- The pool table is represented with a top-down view.
- A cue ball is shown moving towards and bouncing away from the rail.
- The angle of incidence before impact is labeled as \( \theta_1 \).
- The angle of reflection after impact is labeled as \( \theta_2 \).
- Axes are labeled as \( x \) (horizontal) and \( y \) (vertical).
**Text Transcription**
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 \( v_i \) 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 \( \theta_2 \)?
\[ \theta_2 = \text{\underline{\hspace{2cm}}} \]
(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.)
\[ \Delta \vec{p} = \text{\underline{\hspace{2cm}}} \, \hat{\imath} + \text{\underline{\hspace{2cm}}} \, \hat{\jmath} \]
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