Question

You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You can either catch the object or deflect the object back towards 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 MINIMIZE your speed on the skateboard?
Choose one of the following three answers.
A) Your final speed on the skateboard will be the same regardless whether you catch the ball or deflect the ball.
B) You should catch the hall.
B) You should deflect the ball

Answer 1

Answer:

B) You should catch the ball.

Explanation:

In order to minimize the speed on the skateboard, you should catch the ball.

Let 'M' be the mass of the ball, 'm' the mass of the skater, 'V0' the speed the ball was thrown and 'Vs' the speed of the skater.

By conservation of momentum, if the skater catches the ball:

$M*V_{0} + m*0 = (m+M)*V_{s}\\V_{s} = \frac{M*(V_{0} - V_{s})}{(m)}$

If the skater deflects the ball, it will assume a new velocity with direction opposite to that of the skater, let it be 'Vb':

$M*V_{0} + m*0 = m*V_{s}-M*V_{b}\\V_{s} = \frac{M*V_{0}+ M*V_{b}}{(m)}\\V_{s} = \frac{M(V_{0}+ V_{b})}{m}$

Since:

$V_{0} - V_{s} < V_{0}+ V_{b}$

A lower velocity would be achieved by catching the ball.