A child drops a ball. The ball hits the ground and bounces. The graph to the left shows the velocity-time graph for the ball from when the ball is dropped until when the ball reaches the top of its first bounce. Air resistance has been ignored. When the ball hits the ground, energy is transferred from the ball to the Earth. Explain how the data in the graph above shows this energy transfer.

We can see that is the graph that if a child release the ball above the ground at A, it hits the ground at B. Bounces back with a reaches the top again at C, and hits the ground again at D.

The slope of velocity time graph represents acceleration. From A to B, velocity in increasing constantly with respect to time, which means constant acceleration from A to B. AS velocity increase, momentum of the ball also increases, which results in the increase of Kinetic energy.

At B, the ball hits the ground, the velocity decreases, momentum decrease s, because kinetic energy is transferred from the ball to the ground, due to which the ball would not attain the same height after the bounce.

Then the velocity remains negative at C, which means that now the ball is moving in opposite direction till C. It reaches its new at height at C, which is not the same as that of A because of lost in Kinetic Energy, and fall again.