Question

When serving a tennis ball, a player hits the ball when its velocity is zero (at the highest point of a vertical toss). The racquet exerts a force of 565 N on the ball for 5.1 ms, giving it a final velocity of 47.5 m/s. What is the initial velocity of the ball?

Answer 1

Using the impulse-momentum theorem, the mass of the tennis ball is found to be 0.06 kg by applying the exerted force and change in velocity.

Step-by-step explanation:

When a tennis player serving a ball exerts a force on the ball, we can use Newton's second law of motion and the impulse-momentum theorem to calculate the mass of the ball. According to the problem, the racquet exerts a force of 540 N for 5.00 ms (0.005 seconds), giving the ball a final velocity of 45.0 m/s. Since the initial velocity is zero, the change in velocity (Δv) is simply the final velocity, which is 45.0 m/s.

To calculate the mass (m) of the ball, we use the impulse-momentum theorem, which states that the impulse (force times time) is equal to the change in momentum (mass times change in velocity).

Impulse = Force × Time = Change in momentum = mass × Δv

In mathematical terms, the equation is:
540 N × 0.005 s = m × 45.0 m/s

Solving for m:
m = (540 N × 0.005 s) / 45.0 m/s
m = 0.06 kg

The mass of the tennis ball is therefore 0.06 kg (60 grams).