Answer to Question #95054 in Physics for Paul

Question

An anstranaut on the moon picks up a rock and holds it out. At that moment, the rock is at rest and has 5.00 joules of gravitational potential energy. A moment later the rock hit the surface of the moon. What was the kinetic energy of the rock immediately before it hits the surface of the moon?

Answer 1

Total energy of the rock is the sum of kinetic and potential energies: $E = T + U = const$ (this quantity is conserved).

In the first state, the rock is at rest (has zero kinetic energy) and has gravitational potential energy $5 J$, and just before it hits the surface of the moon, it has zero potential energy, and some kinetic energy. By the law of the conservation of total energy, $0 + 5 J = T + 0$, so just before the rock hits the surface, it has kinetic energy $5 J$.