Final answer:
The change in momentum of a ball after an elastic collision is in the upward direction, opposite to its initial momentum. Earth experiences an equal and opposite change in momentum, but with an imperceptible change in velocity. Energy loss during a collision is due to the transformation into other forms like sound or heat.
Step-by-step explanation:
The question pertains to the concept of momentum in the context of an elastic collision in physics.
During an elastic collision, like a ball bouncing off the floor, the direction of the change in momentum of the ball is directly opposite to the momentum it had before colliding with the floor.
Since momentum is a vector and is proportional to both mass and velocity, the ball's change in momentum can be represented by its initial velocity downwards just before impact (minus), and its velocity upwards just after impact (plus).
Hence, if we define the downward direction as negative and upwards as positive, the change in momentum would be in the positive direction.
For the Earth's change of momentum, according to Newton's third law of motion, the Earth experiences an equal and opposite change in momentum. However, due to its massive size, the change in Earth's velocity would be negligible.
Regarding the energy loss, when a ball does not return to its original height, it suggests that some kinetic energy was lost during the collision, mainly transformed into other forms of energy such as sound or heat.