A bowling ball rolling on level ground at the speed v strikes a basketball at rest. The basketball moves off in the original direction of the bowling ball
A) with the speed v while the bowling ball stops.
B) faster than v while the bowling ball continues slower than v.
C) with the speed v while the bowling ball moves backward.
D) together with the bowling ball at the same speed of less than v.

Question

Quizplus · Accepted Answer

This scenario can be modeled using conservation of momentum. Before the collision, the total momentum is mv, where m is the mass of the bowling ball and v is its velocity. After the collision, the total momentum is still mv, but it is shared between the basketball and the bowling ball. Let's assume the basketball has a mass of M. Then, we can write:

mv = Mv_basketball + m*v_bowling ball

Since the basketball is at rest before the collision, v_bowling ball = v. Solving for v_basketball, we get:

v_basketball = (m/M)*v

Therefore, the basketball moves faster than the bowling ball (since m/M < 1), but both objects move in the same direction. Thus, choice B is the correct answer. Choice A is incorrect because the bowling ball wouldn't stop unless there was friction acting on it. Choice C is incorrect because the bowling ball can't move backward unless there is a force acting in that direction. Choice D is incorrect because we know from the conservation of momentum equation that the two objects must move at different speeds.

A Bowling Ball Rolling on Level Ground at the Speed