A tennis ball has a velocity of 25 m/s and a mass of 57.5 g. After the ball hits a tennis racket, the velocity becomes twice that of the original speed and goes in the opposite direction. What is the force between the ball and the racket if the time that they interact is 0.07 s? Assume the force is constant.

To find the force between the ball and the racket, we can use Newton's second law of motion, which states that force (F) is equal to the rate of change of momentum (mv):

F = Δp / Δt

Where:
F is the force,
Δp is the change in momentum, and
Δt is the time interval.

To calculate the force, we need to find the change in momentum of the tennis ball. We can calculate the initial momentum (p1) and final momentum (p2) of the ball using the formula:

momentum (p) = mass (m) × velocity (v)

Initial momentum:
p1 = m × v1

Final momentum:
p2 = m × v2

Given:
Initial velocity (v1) = 25 m/s
Mass of the ball (m) = 57.5 g = 0.0575 kg
Final velocity (v2) = 2 × initial velocity = 2 × 25 m/s = 50 m/s
Time interval (Δt) = 0.07 s

Calculating the initial momentum:
p1 = m × v1
= 0.0575 kg × 25 m/s

Calculating the final momentum:
p2 = m × v2
= 0.0575 kg × 50 m/s

Now, we can calculate the change in momentum (Δp):
Δp = p2 - p1

Finally, we can find the force (F) using the formula:
F = Δp / Δt

With these values, you can plug them into the formulas and calculate the force between the ball and the racket.