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 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?

You should deflect the ball in order to maximize your speed on the skateboard.

Since this creates a larger impulse, you want to deflect the ball. Splitting it up into catching and throwing the ball may by something you can think of deflecting the ball. First, you need to catch the ball, which in turn would push you forward with some speed. (The speed we are talking about should obviously be equal to option A, where you catch the ball). Now, throw the ball back to him since these two processes are equal to deflecting the ball. Throwing a mass away from you would cause or enable you to move even fast.