Aball is thrown upward. at a height of 10 meters above the ground, the ball has a potential energy of 50 joules (with the potential energy equal to zero at ground level) and is moving upward with a kinetic energy of 50 joules. what is the maximum height h reached by the ball?

The maximum height reached by the ball is 20 meters.

By the principle of energy conservation, total mechanical energy of the ball () is conserved in every time and part of the motion and that energy is the sum of the gravitational potential energy () and the translational kinetic energy (). All energy components are measured in joules.

Please remind that gravitational potential energy is directly proportional to the height of the ball (), in meters. Then, the total energy and the maximum height reached by the ball are, respectively:

(1)

(2)

The maximum height reached by the ball is 20 meters.

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The maximum height reached by the ball is 20 m.

Given data:

The height above the ground is, h = 10 m.

The potential energy is, PE = 50 J.

The kinetic energy at ground is, KE = 50 J.

According to conservation of energy, "The total mechanical energy is equal to sum of kinetic energy and potential energy at any point".

ME = KE + PE

ME = 50 J + 50 J

ME = 100 J.

Since, at maximum height, the entire mechanical energy is due to potential energy at that point .

Mechanical energy at maximum height = potential energy at maximum height

ME = PE'

ME = mgH ........................................(1)

Here m is the mass of body,

Substituting the value in equation (1) as,

Thus, the maximum height reached by the ball is 20 m.

Learn more about conservation of energy here:

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has mass of one amu