What is the relationship between the height from which a ball is dropped and the height it bounces back?

The relationship between the height from which a ball is dropped and the height it bounces back largely depends on the material properties of the ball and the surface it strikes. When a ball is dropped from a certain height, it accelerates due to gravity until it hits the ground, gaining kinetic energy. Upon impact, some of this energy is converted back into potential energy as the ball deforms and then rebounds.

In general, the more height from which a ball is dropped, the more kinetic energy it will have at the moment of impact, resulting in a greater bounce height, assuming the ball is elastically deformed and energy losses due to factors like air resistance and heat are minimal. However, this relationship can exhibit diminishing returns at extremely high drop heights or with certain materials that may not regain all their energy.

Thus, it is reasonable to conclude that the bounce height does indeed increase significantly with the drop height, reflecting a positive correlation affected by physical laws governing energy conservation.