Answer:We can use the impulse-momentum theorem to find the average force exerted by the racket on the ball:
impulse = change in momentum
The impulse can be calculated as the product of the force and the time during which the force is applied:
impulse = force × time
We can rearrange the first equation to solve for the force:
force = impulse / time
We can find the impulse by calculating the change in momentum of the ball:
change in momentum = final momentum - initial momentum
The initial momentum of the ball is:
p1 = m × v1 = 0.060 kg × 15 m/s = 0.9 kg m/s
The final momentum of the ball is:
p2 = m × v2 = 0.060 kg × (-10 m/s) = -0.6 kg m/s
The negative sign indicates that the direction of the momentum is opposite to the initial direction, as the ball rebounds in the opposite direction.
The change in momentum is:
Δp = p2 - p1 = -0.6 kg m/s - 0.9 kg m/s = -1.5 kg m/s
The impulse is equal to the change in momentum:
impulse = Δp = -1.5 kg m/s
The time during which the force is applied is:
t = 0.030 s
Therefore, the average force exerted by the racket on the ball is:
force = impulse / time = (-1.5 kg m/s) / (0.030 s) = -50 N
The negative sign indicates that the force is in the opposite direction to the initial direction of the ball. The magnitude of the force is 50 N.
Step-by-step explanation: