A baseball on a T-ball stand has no momentum until it is hit with a bat. When Tyler swings the bat, it has a momentum of 12 kg m/s. After the bat hits the ball, the ball has a momentum of 8 kg m/s. What is the momentum of the bat AFTER it hits the ball?

A) 0 kg m/s

B) 4 kg m/s

C) 5 kg m/s

D) 8 kg m/s

4 kg m/s (option B)

Explanation:

We use conservation of momentum to solve this problem.

In the initial state, the ball has momentum zero (no momentum), and the bat has a momentum of 12 kg m/s.

Since the momentum of the system that interacts ("bat plus ball"), has to be conserved (that means the final total momentum must equal the initial total momentum), we have:

Total initial momentum = 0 kg m/s + 12 kg m/s = 12 kg m/s

Total final momentum = 8 kg m/s + X

where X is our unknown: the final momentum of the bat, and 8 kg m/s is the final momentum of the ball.

We make these two quantities equal since the total momentum has to e conserved, and solve for the unknown X in the equation:

Total initial momentum = Total final momentum

12 kg m/s = 8 kg m/s + X

12 kg m/s - 8 kg m/s = X

X = 4 kg m/s