A tennis ball with a speed of 27.8 m/s is
moving perpendicular to a wall. After striking
the wall, the ball rebounds in the opposite
direction with a speed of 20.016 m/s.
If the ball is in contact with the wall for
0.0133 s, what is the average acceleration of
the ball while it is in contact with the wall?
Take “toward the wall” to be the positive
direction.
Answer in units of m/s^2
To find the average acceleration of the ball while it is in contact with the wall, we can use the following formula:
Average acceleration = (Change in velocity) / (Time taken)
The change in velocity can be calculated by subtracting the initial velocity (velocity before striking the wall) from the final velocity (velocity after rebounding from the wall).
Change in velocity = Final velocity - Initial velocity
From the information given, the initial velocity of the ball is 27.8 m/s (moving perpendicular to the wall) and the final velocity is -20.016 m/s (since the ball rebounds in the opposite direction).
Change in velocity = -20.016 m/s - 27.8 m/s
Now, we need to determine the time taken. Given that the ball is in contact with the wall for 0.0133 s, we can use this value as the time taken.
Average acceleration = (Change in velocity) / (Time taken)
Average acceleration = (-20.016 m/s - 27.8 m/s) / (0.0133 s)
Simplifying the calculation:
Average acceleration = (-47.816 m/s) / (0.0133 s)
Finally, we can divide these values to find the average acceleration:
Average acceleration ≈ -3594.74 m/s^2
Therefore, the average acceleration of the ball while it is in contact with the wall is approximately -3594.74 m/s^2. (Note: The negative sign indicates that the acceleration is in the opposite direction of the initial velocity, i.e., toward the wall.)