An object is released from rest when it is a height h above the surface of a planet of mass M and radius R. What is the speed of the object just before striking the surface of the planet? Neglect any air resistance. Let h = 4.0 * 106 m, R = 5.0 * 106 m, and M = 4.0 * 1024 kg.
A)7.8 km/s
B)3.5 km/s
C)5.4 km/s
D)6.9 km/s
E)4.8 km/s

Question

Quizplus · Accepted Answer

Using conservation of energy:
Initial energy = mgh
Final energy = 1/2 mv^2 - GMm/R
Setting them equal and solving for v:
v = sqrt(2GM/R + 2gh) = 6.9 km/s (rounded to one decimal place)

An Object Is Released from Rest When It Is a Height