If the ball were to strike the floor, hit the ground and rebound as in an inelastic collision, it would follow that the total momentum of the Earth and the ball is conserved. However, in the inelastic collision, some of its kinetic energy becomes other types of energy like heat or sound that causes loss of mechanical energy but the system with both Earth and the ball together conserves their total momentum.

This is a basic principle in physics, which states that the total momentum of a closed system remains constant if no external forces act upon it. In this case, the ball and the Earth constitute a closed system, and the internal forces during the collision do not affect the total momentum.

Note that, although momentum is conserved, mechanical energy is not in inelastic collisions because kinetic energy is converted into other forms of energy. Thus, the correct answer is that the total momentum of the ball and the Earth is conserved.

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