Kaplan 10th Edition DT Q54

Kaplan's Book

54) This question asks us to find the impulse (change in momentum) of the ball after hitting the wall. First, it is crucial to realize that the problem states that the ball bounces off elastically. When I read this, "bounces off" tells me that the final velocity will be in the opposite direction, and "elastically" tells me that kinetic energy of the system is conserved. Let's write an equation for the conservation of kinetic energy.

Where K is kinetic energy, m is mass, and v is speed

Since the mass of the ball is constant, the speed of the ball before and after bouncing off the wall must be the same.

However, as we discussed before, the ball bounces off the wall, so the velocity will be in the opposite direction. We can consider the final velocity as -v because it is of the opposite direction.

We have all we need to find the change in momentum.

Where J is impulse, p is momentum, m is mass, and v is velocity

The question just asks for the change in momentum so our answer is 2mv.

Answer: B