You are standing on a skateboard,initially at rest.A friend throws a very heavy ball toward you.You can either catch the object or deflect the object back toward your friend (such that it moves away from you with the same speed as it was originally thrown).What should you do in order to maximize your speed on the skateboard?

Question

Quizplus · Accepted Answer

According to the law of conservation of momentum, the total momentum of the system (you, skateboard, and ball) remains constant if no external forces act on it. When your friend throws the ball, the ball has momentum in one direction, and the skateboard and you are at rest, so the total momentum is zero. If you catch the ball, its momentum becomes zero, and your momentum remains zero. Hence, your final velocity on the skateboard would be zero.

However, if you deflect the ball back towards your friend, the momentum of the ball changes direction, but its magnitude remains the same. Therefore, if you deflect it back with the same speed, the ball's momentum and your momentum combined will be conserved and equal to zero. Since you were initially at rest, the total momentum after the ball is deflected back is just the magnitude of the ball's momentum divided by your mass. Hence, your final velocity is equal to the magnitude of the ball's momentum divided by your mass. Therefore, to maximize your speed on the skateboard, you should deflect the ball back.

You Are Standing on a Skateboard,initially at Rest