Question 3-c, Numerical: Consider the collision of a bouncing tennis ball with a wall as sketched in the figure. if the mass of the tennis ball is 58 g, its initial speed v-180 m/s and its speed after impact is v= 120 m/s. If the time of impact is 0.08 s, what is the average force of impact measured in N? - +x MacBook Air * esc F2 F6 80 F3 a F4 FS 8 F7 DII FB F9

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### Question 3-c, Numerical:

**Problem Statement:**
Consider the collision of a bouncing tennis ball with a wall as sketched in the figure. If the mass of the tennis ball is 58 g, its initial speed \(v_i = 180 \, \text{m/s}\) and its speed after impact is \(v_f = 120 \, \text{m/s}\). If the time of impact is \(0.08 \, \text{s}\), what is the average force of impact measured in N?

**Diagram Explanation:**
- The diagram shows a tennis ball before and after it hits a wall.
- The initial speed of the ball \(v_i\) is directed towards the wall.
- After hitting the wall, the ball's speed decreases to \(v_f\) and is directed away from the wall.
- The time of impact with the wall is \(0.08 \, \text{s}\).

**Notes for understanding:**
- The ball's mass (\(m\)) = \(58 \, \text{g}\) (convert to kg for calculations: \(0.058 \, \text{kg}\)).
- \(v_i\) = \(180 \, \text{m/s}\)
- \(v_f\) = \(120 \, \text{m/s}\)
- \(t\) (time of impact) = \(0.08 \, \text{s}\)

To solve for the average force of impact, use the following steps:

1. **Calculate the change in velocity (\(\Delta v\)):**
   \[
   \Delta v = v_f - v_i
   \]

2. **Calculate the average acceleration (\(a\)):**
   \[
   a = \frac{\Delta v}{t}
   \]

3. **Use Newton's Second Law (F = ma) to find the average force of impact:**
   \[
   F = m \cdot a
   \]

Finally, ensure the answer is in Newtons (N).
Transcribed Image Text:### Question 3-c, Numerical: **Problem Statement:** Consider the collision of a bouncing tennis ball with a wall as sketched in the figure. If the mass of the tennis ball is 58 g, its initial speed \(v_i = 180 \, \text{m/s}\) and its speed after impact is \(v_f = 120 \, \text{m/s}\). If the time of impact is \(0.08 \, \text{s}\), what is the average force of impact measured in N? **Diagram Explanation:** - The diagram shows a tennis ball before and after it hits a wall. - The initial speed of the ball \(v_i\) is directed towards the wall. - After hitting the wall, the ball's speed decreases to \(v_f\) and is directed away from the wall. - The time of impact with the wall is \(0.08 \, \text{s}\). **Notes for understanding:** - The ball's mass (\(m\)) = \(58 \, \text{g}\) (convert to kg for calculations: \(0.058 \, \text{kg}\)). - \(v_i\) = \(180 \, \text{m/s}\) - \(v_f\) = \(120 \, \text{m/s}\) - \(t\) (time of impact) = \(0.08 \, \text{s}\) To solve for the average force of impact, use the following steps: 1. **Calculate the change in velocity (\(\Delta v\)):** \[ \Delta v = v_f - v_i \] 2. **Calculate the average acceleration (\(a\)):** \[ a = \frac{\Delta v}{t} \] 3. **Use Newton's Second Law (F = ma) to find the average force of impact:** \[ F = m \cdot a \] Finally, ensure the answer is in Newtons (N).
### Question 3-b, Numerical:

Consider the collision of a bouncing tennis ball with a wall as sketched in the figure. If the mass of the tennis ball is 58.0 g, its initial speed \( v_i = 180 \, \text{m/s} \) and its final speed, after impact, is \( v_f = 120 \, \text{m/s} \). What is the impulse acting on the ball during the impact measured in \( \text{N} \cdot \text{s} \)?

**Graph/Diagram Explanation:**

The diagram illustrates a tennis ball colliding with a wall. The ball is shown moving towards the wall with an initial velocity \( v_i \) and then rebounding with a final velocity \( v_f \). Notably, the direction of the initial velocity is towards the wall, represented by a vector pointing to the right, while the final velocity direction is away from the wall, represented by a vector pointing to the left. The coordinate axis shows the positive \( +x \) direction to the right, aligning with the initial velocity direction.
Transcribed Image Text:### Question 3-b, Numerical: Consider the collision of a bouncing tennis ball with a wall as sketched in the figure. If the mass of the tennis ball is 58.0 g, its initial speed \( v_i = 180 \, \text{m/s} \) and its final speed, after impact, is \( v_f = 120 \, \text{m/s} \). What is the impulse acting on the ball during the impact measured in \( \text{N} \cdot \text{s} \)? **Graph/Diagram Explanation:** The diagram illustrates a tennis ball colliding with a wall. The ball is shown moving towards the wall with an initial velocity \( v_i \) and then rebounding with a final velocity \( v_f \). Notably, the direction of the initial velocity is towards the wall, represented by a vector pointing to the right, while the final velocity direction is away from the wall, represented by a vector pointing to the left. The coordinate axis shows the positive \( +x \) direction to the right, aligning with the initial velocity direction.
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