A tennis ball with a speed of 28.3 m/s is
moving perpendicular to a wall. After striking
the wall, the ball rebounds in the opposite
direction with a speed of 14.6311 m/s.
If the ball is in contact with the wall for0.013 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
.
Why did the tennis ball bring a calculator to the wall? Because it wanted to calculate the average acceleration! Now let's do some math and find the answer.
To find the average acceleration, we can use the equation:
average acceleration = (change in velocity) / (time)
The change in velocity is the difference between the initial speed and the rebound speed. So, it will be:
change in velocity = initial speed - rebound speed
Substituting the given values:
change in velocity = 28.3 m/s - 14.6311 m/s
Now, let's divide the change in velocity by the time:
average acceleration = (28.3 m/s - 14.6311 m/s) / 0.013 s
Calculating...
average acceleration ≈ 999.469 m/s²
So, the average acceleration of the ball while it is in contact with the wall is approximately 999.469 m/s².
To find the average acceleration of the ball while it is in contact with the wall, we need to use the equation:
average acceleration = change in velocity / time
Since the ball reverses its direction after hitting the wall, the change in velocity is the difference between the initial velocity (28.3 m/s towards the wall) and the final velocity (-14.6311 m/s away from the wall). We take the negative sign for the final velocity because it is in the opposite direction.
change in velocity = final velocity - initial velocity
change in velocity = -14.6311 m/s - 28.3 m/s
change in velocity = -42.9311 m/s
The time of contact with the wall is given as 0.013 s.
average acceleration = (-42.9311 m/s) / (0.013 s)
average acceleration ≈ -3302.39 m/s^2
Therefore, the average acceleration of the ball while it is in contact with the wall is approximately -3302.39 m/s^2.
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)
In this case, the change in velocity is the difference between the final velocity and the initial velocity of the ball. The initial velocity is +28.3 m/s (towards the wall) and the final velocity is -14.6311 m/s (opposite direction). The time during which the ball is in contact with the wall is given as 0.013s.
So, the average acceleration can be calculated as follows:
average acceleration = (-14.6311 m/s - 28.3 m/s) / 0.013s
average acceleration = (-42.9311 m/s) / 0.013s
Now, dividing the velocities by the time:
average acceleration = -3310.08 m/s^2
Therefore, the average acceleration of the ball while in contact with the wall is -3310.08 m/s^2. Note that the negative sign indicates that the acceleration is in the opposite direction to the initial velocity (towards the wall).
acceleration = (change in velocity) / time
a = (-14.6311 m/s - 28.3 m/s) / 0.013 s
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