Question

3.2.2 quiz: momentum
question 2 of 10
a 0.057 kg tennis ball and a tennis racket collide. the racket has an initial momentum of -1.75 kg·m/s and a final momentum of -1.25 kg·m/s. the ball has an initial momentum of 0.00684 kg·m/s. if you assume the collision is elastic, what is the final velocity of the ball?
a. -52.48 m/s
b. -8.65 m/s
c. -2.99 m/s
d. -0.50 m/s

Explanation:

Step1: Apply conservation of momentum

In an elastic - collision, the total initial momentum equals the total final momentum. Let $p_{r1}$ be the initial momentum of the racket, $p_{r2}$ be the final momentum of the racket, $p_{b1}$ be the initial momentum of the ball, and $p_{b2}$ be the final momentum of the ball. Then $p_{r1}+p_{b1}=p_{r2}+p_{b2}$.
We know that $p_{r1}=- 1.75\ kg\cdot m/s$, $p_{r2}=-1.25\ kg\cdot m/s$, and $p_{b1}=0.00684\ kg\cdot m/s$.
So, $-1.75 + 0.00684=-1.25 + p_{b2}$.

Step2: Solve for the final momentum of the ball

Rearrange the equation from Step 1 to find $p_{b2}$:
$p_{b2}=-1.75 + 0.00684+1.25=-0.49316\ kg\cdot m/s$.

Step3: Use the momentum - velocity relationship

The momentum formula is $p = mv$, where $m = 0.057\ kg$ is the mass of the ball and $p = p_{b2}$ is the final momentum of the ball. We want to find the final velocity $v$.
$v=\frac{p_{b2}}{m}=\frac{-0.49316\ kg\cdot m/s}{0.057\ kg}\approx - 8.65\ m/s$.

Answer:

B. -8.65 m/s