# How can momentum be conserved in an inelastic collision?

Say I drop a ball of mass 5kg from a height of 2 meters, assuming no air resistance, it will hit the ground with a velocity of 6.26m/s and collide with the ground, and rebound. From the law of conservation of momentum, 6.26 * 5 = v * 5, where v is the new velocity of the ball. But if the ball has lost kinetic energy, then through Ek = 0.5 * 5 * v^2, doesn't this mean the velocity of the ball has decreased? And as a result, it is impossible for momentum to be conserved?

A.T.
Say I drop a ball of mass 5kg from a height of 2 meters, assuming no air resistance, it will hit the ground with a velocity of 6.26m/s and collide with the ground, and rebound. From the law of conservation of momentum, 6.26 * 5 = v * 5, where v is the new velocity of the ball. But if the ball has lost kinetic energy, then through Ek = 0.5 * 5 * v^2, doesn't this mean the velocity of the ball has decreased? And as a result, it is impossible for momentum to be conserved?
The total momentum of ball & Earth is conserved. The momentum of the ball alone isn't conserved even if it rebounds with the same speed, because the direction of momentum changes.

The total momentum of ball & Earth is conserved. The momentum of the ball alone isn't conserved even if it rebounds with the same speed, because the direction of momentum changes.
So the earth has also gained some momentum as a result from the collision, thus balancing the momentum before and after the impact? That makes sense, thanks.

A.T.
So the earth has also gained some momentum as a result from the collision, thus balancing the momentum before and after the impact?
Yes, that is basically what Newtons 3rd Law is about. There are equal but opposite forces on Earth & ball. So the changes in their momentum are also equal but opposite. Hence the total momentum doesn't change.

HallsofIvy