Two skaters,both of mass 75 kg,are initially at rest on skates on a frictionless ice pond.One skater throws a 0.3-kg ball at 10 m/s to his friend,who catches it and throws it back at 10 m/s.When the first skater has caught the returned ball,what is the velocity of each of the two skaters?
A) 0.08 m/s,moving apart
B) 0.04 m/s,moving apart
C) 0.08 m/s,moving towards each other
D) 0.04 m/s,moving towards each other

Question

Quizplus · Accepted Answer

Explanation:Momentum is conserved, so the total momentum of the system (two skaters and ball) is zero before and after the ball is thrown. Initially, both skaters are at rest, so the total momentum is zero. After the first skater throws the ball, the ball has momentum of 0.3 kg * 10 m/s = 3 kg*m/s. To conserve momentum, the first skater must have equal and opposite momentum, so he will move in the opposite direction at a speed of 3 kg*m/s / 75 kg = 0.04 m/s. When the second skater catches the ball and throws it back, the ball again has momentum of 3 kg*m/s, but this time in the opposite direction. To conserve momentum, the second skater must have equal and opposite momentum, so he will move in the same direction as the first skater at a speed of 3 kg*m/s / 75 kg = 0.04 m/s. Therefore, the final velocity of each skater is 0.04 m/s, and they are moving apart.

Two Skaters,both of Mass 75 Kg,are Initially at Rest on Skates