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. if big bill's opponent returned his serve with a speed of 55 m/s , what is the x -component of the impulse he exerted on the ball, assuming only horizontal motion? a) Conservation of momentum

b) Newton's third law
c) Impulse-momentum theorem
d) Kinetic energy equation

Answer 1

The x-component of the impulse exerted on the tennis ball by big bill's opponent when returning the serve is calculated using the impulse-momentum theorem, resulting in an impulse of -7.296 kg·m/s, with the negative sign indicating the opposite direction of the tennis serve.

Step-by-step explanation:

The question is asking for the x-component of the impulse exerted on a tennis ball by big bill's opponent when returning a serve. According to the impulse-momentum theorem, impulse is equal to the change in momentum of the object. The momentum of the ball when served by big bill is its mass times the velocity (57 g × 73 m/s) and the momentum when returned is the mass times the return velocity (57 g × -55 m/s), with the negative sign indicating the opposite direction. The change in momentum, hence the impulse, is the difference between these two.

Calculating the impulse:

• Initial momentum (big bill serve) = 0.057 kg × 73 m/s = 4.161 kg·m/s
• Final momentum (opponent return) = 0.057 kg × (-55 m/s) = -3.135 kg·m/s
• Change in momentum (impulse) = Final momentum - Initial momentum = -3.135 kg·m/s - 4.161 kg·m/s = -7.296 kg·m/s

The negative sign indicates that the direction of the impulse is opposite to the direction of the serve.