A boulder is raised above the ground, so that its potential energy relative to the ground is 200 J. Then it is dropped. Estimate what its kinetic energy will be just before hitting the ground.

200 J

Explanation:

In this problem, I assume there is no air resistance, so the  system is isolated (=no external forces).

For an isolated system, the total mechanical energy is constant, and it is given by:

where

KE is the kinetic energy

PE is the potential energy

The kinetic energy is the energy due to the motion of the object,  while the potential energy is the energy due to the position of the object relative to the ground.

At the beginning, when the boulder is raised above the ground, its height above the ground is maximum, while its  speed is zero; it means that all its mechanical energy is just potential energy, and it is:

As the boulder falls  down, its altitude decreases, so its potential energy decreases, while the speed increases, and the kinetic energy increases. Therefore, potential energy is converted into kinetic energy.

Eventually, just before the boulder hits the ground, the height of the object is zero, and the speed is maximum; this means that all the energy has now converted into kinetic energy, and we have

Therefore, the kinetic energy just before hitting the ground is 200 J.

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