Question

Standing still on a skateboard, you catch a ball tossed horizontally to you. The mass of the ball is one-tenth your mass. Compare with the speed of the caught ball, the speed that both you and the caught ball acquire is about

A) The same 1/100 as much

B) 1/100 as much

C)1/10 as much

D) 10 times as much

E) 100 times as much

I Know the answer is (c) 1/10th as much but will you explain why.

Answer 1

Let the mass of the ball be m and let the speed of the ball be v

Therefore initial momentum = mv

When the ball is caught the mass at that time is m +10m (as the mass of skater is 10 times the ball) = 11m. Let the speed after catching be v'

By law of conservation of momentum

Therefore the the speed after catching is 1/11^th of the speed of ball. Close enough is 1/10^th of ball.

So answer is Option C) 1/10^th