A tennis ball with a speed of 15.1 m/s is
moving perpendicular to a wall. After striking
the wall, the ball rebounds in the opposite
direction with a speed of 7.9577 m/s.
If the ball is in contact with the wall for
0.0139 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.
acceleration equals ... Δv / t = (15.1 - -7.9577) / .0139
watch your significant figures
To find the average acceleration of the ball while it is in contact with the wall, we can use the formula:
Average acceleration = change in velocity / time taken
First, let's calculate the change in velocity:
Change in velocity = final velocity - initial velocity
The initial velocity is 15.1 m/s (toward the wall) and the final velocity is -7.9577 m/s (opposite direction). Hence,
Change in velocity = -7.9577 m/s - 15.1 m/s
Change in velocity = -23.0577 m/s
Next, we need to calculate the time taken, which is given as 0.0139 s.
Now that we have both the change in velocity and the time taken, we can calculate the average acceleration:
Average acceleration = (-23.0577 m/s - 15.1 m/s) / 0.0139 s
Average acceleration = -38.1577 m/s / 0.0139 s
Using a calculator, we can find:
Average acceleration = -2746.9166 m/s^2
Therefore, the average acceleration of the ball while it is in contact with the wall is approximately -2746.9166 m/s^2.
To find the average acceleration of the ball while in contact with the wall, we can use the formula:
Average acceleration = (Change in velocity) / (Time taken)
Here, the initial velocity of the ball before hitting the wall is 15.1 m/s, and the final velocity after rebounding is -7.9577 m/s (since it moves in the opposite direction). The time taken for contact with the wall is given as 0.0139 s.
To calculate the change in velocity, we subtract the final velocity from the initial velocity:
Change in velocity = final velocity - initial velocity
Change in velocity = (-7.9577 m/s) - (15.1 m/s)
Now, we can substitute the values into the formula to find the average acceleration:
Average acceleration = (Change in velocity) / (Time taken)
Average acceleration = [(-7.9577 m/s) - (15.1 m/s)] / 0.0139 s
Calculating the numerator:
(-7.9577 m/s) - (15.1 m/s) = -23.0577 m/s
Substituting this value into the formula:
Average acceleration = (-23.0577 m/s) / 0.0139 s
Calculating the average acceleration:
Average acceleration ≈ -1659.136 m/s^2
Therefore, the average acceleration of the ball while in contact with the wall is approximately -1659.136 m/s^2. Note that the negative sign indicates that the acceleration is directed towards the wall.