10. A soccer ball is kicked toward a goalie and is caught. The goalie brings the ball to rest using her hands. Which of the following statements best describes the impulse ( $$ \bar{J} $$ ) between the ball and the goalie's hands during the catch? A. The impulse experienced by the ball is equal to the change in the ball's linear momentum. B. The impulse experienced by the ball is equal to the average force applied by the goalie divided by the time of contact. C. The impulse experienced by the ball is equal to the change in the ball's velocity. D. No impulse is involved because the ball is brought to rest. E. The impulse experienced by the ball is equal to the average force applied by the goalie multiplied by the distance over which the average force is applied.

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UpStudy AI · Accepted Answer

To determine which statement best describes the impulse ($$ \bar{J} $$) between the soccer ball and the goalie's hands during the catch, let's analyze the concept of impulse and its relationship with momentum.

Impulse is defined as the change in momentum of an object when a force is applied over a period of time. Mathematically, it can be expressed as:

$$
\bar{J} = \Delta p = F_{avg} \cdot \Delta t
$$

where:
- $$ \bar{J} $$ is the impulse,
- $$ \Delta p $$ is the change in momentum,
- $$ F_{avg} $$ is the average force applied,
- $$ \Delta t $$ is the time duration over which the force is applied.

Now, let's evaluate each option:

A. **The impulse experienced by the ball is equal to the change in the ball's linear momentum.**
   - This statement is true because impulse is defined as the change in momentum.

B. **The impulse experienced by the ball is equal to the average force applied by the goalie divided by the time of contact.**
   - This statement is incorrect. Impulse is equal to the average force multiplied by the time of contact, not divided.

C. **The impulse experienced by the ball is equal to the change in the ball's velocity.**
   - This statement is misleading. While impulse is related to the change in velocity through momentum, it is not directly equal to the change in velocity.

D. **No impulse is involved because the ball is brought to rest.**
   - This statement is incorrect. Impulse is involved in bringing the ball to rest.

E. **The impulse experienced by the ball is equal to the average force applied by the goalie multiplied by the distance over which the average force is applied.**
   - This statement is incorrect. Impulse is not defined in terms of distance but rather in terms of force and time.

Based on this analysis, the best description of the impulse between the ball and the goalie's hands during the catch is:

**A. The impulse experienced by the ball is equal to the change in the ball's linear momentum.**
The impulse experienced by the ball is equal to the change in the ball's linear momentum.

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