A ball is dropped from rest at height of 20m. If it loses 25% of its kinetic energy when it strikes the ground. What is the height to which it bounces?

15 meters

Explanation:

The inicial energy of the ball is just potencial energy, and its value is:

E = m * g * h = m * g * 20,

where m is the ball mass, and g is the value of gravity.

In the moment that the ball strickes the ground, all potencial energy transformed into kinetic energy, and 25% of this energy is lost, so the total energy at this moment will be:

E' = 0.75 * E = 0.75 * m * g * 20 = 15*m*g

This kinetic energy will make the ball goes up again, and at the maximum height, all kinetic energy is transformed back into potencial energy.

So, as the mass and the gravity are constants, we can calculate the height the ball will reach:

E' = m*g*h = 15*m*g -> h = 15 meters

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