Question

The mass of a regulation tennis ball is 57 g (although it can vary slightly), and tests have shown that the ball is in contact with the tennis racket for 30 ms . (this number can also vary, depending on the racket and swing.) we shall assume a 30.0 ms contact time. one of the fastest-known served tennis balls was served by "big bill" tilden in 1931, and its speed was measured to be 73 m/s . suppose that the positive direction of the x -axis is along the direction of motion of the ball after big bill's hit. what is the x -component of the impulse exerted by big bill on the tennis ball in his record serve? assume that the initial speed of the ball is zero. a) 0.057 kg m/s

b) 5.61 kg m/s
c) 4.21 kg m/s
d) 3.73 kg m/s

Answer 1

The x-component of the impulse exerted on a regulation tennis ball with a mass of 57 g served at a speed of 73 m/s is 4.21 kg×m/s, which is calculated by multiplying the mass by the final velocity, as the initial speed is zero.

Step-by-step explanation:

The subject of this question deals with calculating the x-component of the impulse exerted on a tennis ball during a serve in a physics context. Impulse is defined as the change in momentum of an object when it is subject to a force over a period of time. Since the mass of a regulation tennis ball is given as 57 g (0.057 kg) and the final velocity after the serve is 73 m/s, we can calculate the impulse using the formula I = m×Δv, where I is impulse, m is mass, and Δv is the change in velocity.

To find the x-component of the impulse, we assume the initial velocity (u) is 0 m/s because the ball is hit from rest. The formula simplifies to I = m × v, where v is the final velocity. Substituting in the given values:

I = 0.057 kg × 73 m/s = 4.161 kg×m/s.

Thus, the x-component of the impulse is approximately 4.21 kg×m/s, which corresponds to option c) 4.21 kg m/s.