Answer
See below.
Work Step by Step
The speed of an object orbiting a planet of mass $M$ from a radius $R$ is equal to $$v=\sqrt{\frac{GM}{R}}$$ Therefore, if the radius above the planet is high (when the person is on the mountain) and the speed of the rock is great enough, the rock will enter orbit. Once it enters orbit and completes a full orbit about the moon, the rock will return to its original location.