A 0.065 kg tennis ball moving to the right with a speed of 15 m/s is struck by a tennis racket, causing it to move to the left with a speed of 15 m/s. If the ball remains in contact with the racquet for 0.020 s, what is the magnitude of the average force experienced by the ball?

Options

A. 0N
B. 98 N
C. 160 N
D. 240 N

Answer

To solve the problem of finding the magnitude of the average force experienced by the tennis ball, we can follow these steps:

### Step 1: Identify the given values
- Mass of the tennis ball (m) = 0.065 kg
- Initial velocity (u) = 15 m/s (to the right)
- Final velocity (v) = -15 m/s (to the left, hence negative)
- Time of contact (Δt) = 0.020 s

### Step 2: Calculate the initial momentum (p_initial)
The initial momentum (p_initial) can be calculated using the formula:
\[ p_{\text{initial}} = m \cdot u \]
Substituting the values:
\[ p_{\text{initial}} = 0.065 \, \text{kg} \cdot 15 \, \text{m/s} = 0.975 \, \text{kg m/s} \]

### Step 3: Calculate the final momentum (p_final)
The final momentum (p_final) can be calculated using the formula:
\[ p_{\text{final}} = m \cdot v \]
Substituting the values:
\[ p_{\text{final}} = 0.065 \, \text{kg} \cdot (-15 \, \text{m/s}) = -0.975 \, \text{kg m/s} \]

### Step 4: Calculate the change in momentum (Δp)
The change in momentum (Δp) is given by:
\[ \Delta p = p_{\text{final}} - p_{\text{initial}} \]
Substituting the values:
\[ \Delta p = -0.975 \, \text{kg m/s} - 0.975 \, \text{kg m/s} = -1.95 \, \text{kg m/s} \]

### Step 5: Calculate the average force (F_average)
The average force can be calculated using the formula:
\[ F_{\text{average}} = \frac{\Delta p}{\Delta t} \]
Substituting the values:
\[ F_{\text{average}} = \frac{-1.95 \, \text{kg m/s}}{0.020 \, \text{s}} = -97.5 \, \text{N} \]

### Step 6: Determine the magnitude of the average force
Since we are interested in the magnitude of the average force, we take the absolute value:
\[ |F_{\text{average}}| = 97.5 \, \text{N} \]

Thus, the magnitude of the average force experienced by the ball is approximately **98 N**.