Question

A bowling ball is dropped from a height h onto the center of a trampoline, which launches the ball back up into the air. How high will the ball rise?

1. Significantly less than h.
2. More than h. The exact amount depends on the mass of the ball and the springiness of the trampoline
3. No more than h—probably a little less.
4. Cannot tell without knowing the characteristics of the trampoline.

Short answer

Option (c): No more than h—probably a little less.

Step-by-step solution

Definition of gravitational potential energy

Potential energy is a scalar quantity. The energy stored in an object by virtue of its position above the surface of the earth is known as gravitational potential energy.

It is given by:

\(PE = mgh\)

Here, m is the mass of the object, h is the height, and g is the acceleration due to gravity \(9.8\;{\rm{m/}}{{\rm{s}}^{\rm{2}}}\).

Analysis of the gravitational potential energy of the ball

There is no external energy given to the ball after it is dropped. So, its final gravitational energy is the same as its initial potential energy.

Analysis of the height achieved by the ball after bouncing back

Suppose, if some energy is lost due to air resistance and heat, the ball will have less gravitational potential energy than the initial one.

This implies that the height achieved by the ball will probably be slightly less than h.