Question

a 0.057 kg tennis ball and a tennis racket collide. the racket has an initial momentum of -3.15 kg·m/s and a final momentum of -2.21 kg·m/s. the ball has an initial momentum of 0.03135 kg·m/s. if you assume the collision is elastic, what is the final velocity of the ball?
a. -93.55 m/s
b. -0.90 m/s
c. -15.94 m/s
d. -5.33 m/s

Explanation:

Step1: Use conservation of momentum

The law of conservation of momentum states that \(p_{i,total}=p_{f,total}\). So, \(p_{i,racket}+p_{i,ball}=p_{f,racket}+p_{f,ball}\).
We can rearrange it to find \(p_{f,ball}\): \(p_{f,ball}=p_{i,racket}+p_{i,ball}-p_{f,racket}\).
Substitute the given values: \(p_{i,racket}=- 3.15\space kg\cdot m/s\), \(p_{i,ball}=0.03135\space kg\cdot m/s\), \(p_{f,racket}=-2.21\space kg\cdot m/s\).
\(p_{f,ball}=-3.15 + 0.03135-(-2.21)\)
\(p_{f,ball}=-3.15 + 0.03135 + 2.21=-0.90865\space kg\cdot m/s\)

Step2: Use the formula for momentum \(p = mv\)

We know \(p = mv\), so \(v=\frac{p}{m}\).
The mass of the ball \(m = 0.057\space kg\) and \(p_{f,ball}=-0.90865\space kg\cdot m/s\).
\(v=\frac{-0.90865}{0.057}\approx - 15.94\space m/s\)

Answer:

C. \(-15.94\space m/s\)