Question: When a basketball player leaps high for the ball, he suddenly gets an upward momentum. How do you reconcile this observation with the law of conservation of momentum?

Answer: In order to jump, the player must push against the floor. In doing so the earth recoils as the player moves up. The momentum imparted to the earth has the same magnitude but opposite direction as that of the player. However, because the mass of the earth is so very much larger than the mass of the player, the earth's recoil velocity is too small to be noticed. Nevertheless, the total momentum is conserved.

Question: At the top of the leap the player's momentum changes direction. How do you reconcile this observation with the law of conservation of momentum?

Answer: The force of gravity acts on the player throughout the jump. It is this force that alters the player's momentum during the jump. If we only consider the motion of the player, then the gravitational force is an external force and the law of momentum conservation is not appropriate. However, let us consider the system that includes both the player and the earth. Gravity acts on each as equal but opposite internal forces in accord with Newton's third law. The combined momentum of the player and the earth remains constant as expected from the law of conservation of momentum: the total momentum of a system is constant when the net external force on the system is zero.