Question

A 57 g tennis ball is thrown upward and then struck just as it comes to rest at the top of its motion. The racket exerts an average horizontal force of magnitude 4.2 x 10^2 N on the tennis ball.

a) Determine the speed of the ball after the collision if the average force is exerted on the ball for 4.5 ms.
b) Repeat the calculation assuming a time interval of 5.3 ms.
c) Explain the meaning and advantage of follow-through in this example.
Options:
A) a) 1.35 m/s, b) 1.2 m/s, c) Follow-through increases accuracy and power.
B) a) 7.5 m/s, b) 8.1 m/s, c) Follow-through minimizes injury.
C) a) 6.5 m/s, b) 5.5 m/s, c) Follow-through reduces vibration.
D) a) 3.7 m/s, b) 2.9 m/s, c) Follow-through enhances balance.

Answer 1

Calculations show that the speed of the tennis ball after being hit by the racket with force applied for 4.5 ms is 33.16 m/s, and for 5.3 ms, it is 39.05 m/s. The follow-through provides both increased accuracy and power by ensuring a smoother transition of the forces involved, as well as reducing the injury risk by allowing the muscles to decelerate naturally.

Step-by-step explanation:

The question is related to physics and involves using Newton's second law and the concept of impulse to calculate the speed of a tennis ball after being struck by a racket. To solve this, we use the formula for impulse, I = Δp (change in momentum), where impulse, I is equal to the force applied multiplied by the time the force is applied, and momentum, p, is the product of mass and velocity. For part a), we have: Force, F = 4.2 x 10^2 N Time, t = 4.5 ms = 4.5 x 10^-3 s The impulse is therefore: I = F × t = (4.2 x 10^2 N) × (4.5 x 10^-3 s) = 1.89 kg·m/s Since the ball starts from rest, the change in momentum is equal to the final momentum: m·v = I, v = I / m = 1.89 kg·m/s / 0.057 kg = 33.16 m/s For part b), with a time interval t = 5.3 ms: I = F × t = (4.2 x 10^2 N) × (5.3 x 10^-3 s) = 2.226 kg·m/s v = I / m = 2.226 kg·m/s / 0.057 kg = 39.05 m/s Part c), regarding the follow-through: Follow-through in tennis serves multiple purposes. By continuing the motion after striking the ball, the player provides a smoother transition of forces, which can help increase the speed and control of the shot, thus improving accuracy and power. It also allows the muscles to slow the racquet over a greater period of time, reducing the risk of injury by not abruptly stopping the motion.