An object with mass m is released from rest at a distance of a meters above the earth’s su...

An object with mass m is released from rest at a distance of a meters above the earth’s surface (see Figure). Use Newton’s universal law of gravitation (see Exercise) to show that the object impacts the earth surface with a velocity determined by

where g is the acceleration due to gravity at the earth’s surface and R is the radius of the earth. Ignore any affects due to the earth’s rotation and atmosphere. Hint: On the earth’s surface, explain why mg = GMm/R2, where M is the mass of the earth and G is the universal gravitational constant.

Figure. The object in Exercise.