Why does a young woman push down on the ground to jump up into the air to get a rebound in a basketball game?

Answer 1

Think of the woman and the Earth as two objects attached physically to each other, or in other words, a system. When the woman jumps she pushes the Earth away from her, giving it a certain momentum.

Now, the law of conservation of momentum states that the total momentum of any system is constant, given that there is no external force acting on it. Before the woman jumps, the total momentum is zero due to the fact that the system isn't moving(with respect to a point of reference, of course). This means that the final momentum after the woman jumps must also be zero. Therefore, the woman must gain the same amount of momentum she gave to the Earth, but in the opposite direction, in order to conserve the total momentum. Note that the woman moves away faster than the Earth does due to her significantly smaller mass.

mass of woman x velocity of woman = mass of earth x velocity of earth