Verified answer

Think of it this way - you will have to absorb the same amount of kinetic energy no matter how you catch it, due to the balls mass and velocity. You have to do an amount of work to stop it (apply a force over a distance) that is equal to the kinetic energy of the ball.

So if you just hold your hand firm and let the ball hit you, you have a small distance that the ball travels, making the force on your hand large. If you move your hand in the direction of the ball's travel, then you increase the distance over which the force acts, which decreases the force.

Moving Fastball

Think of it like an accident...If you're moving in the opposite direction of the car...you know how bad its going to be...if you bump into each other going in the same direction it is nowhere near as bad...