Conservation of Momentum

I had a thought about the problem in the final exam mashup that shows a man throwing a ball while standing on the cart. This problem is dealing with the conservation of linear momentum. As soon as the man throws the ball, he and the cart move to the right and the ball moves to the left. When the ball hits the cart and bounces backward, the man and the cart begin to move to the left. This is because the ball bouncing off the cart is analogous to the cart catching the ball and throwing it backwards.
Another way to state the conservation of linear momentum is: if there are no external forces, the center of mass of a system stays constant. In this case, the center of mass is initially at rest. Since there are no external forces acting in the horizontal direction, and the ball winds up flying to the right, the cart must move to the left in order to keep the x_bar in the same place.