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

The speed of the object just before striking the surface of the planet can be found using the conservation of energy. At height h, the object has potential energy given by
U = G M m / R + G M m / (R + h)
where G is the gravitational constant and m is the mass of the object. At the surface of the planet (h = 0), the object has kinetic energy given by
K = 1/2 m v^2
where v is the speed of the object just before striking the surface. Assuming conservation of energy, we have
U = K
solving for v^2, we get
v^2 = 2 G M / R (1 - 1 / (1 + h/R))
Plugging in the given values, we get v = 6.9 km/s, which is choice (D).

An Object Is Released from Rest When It Is a Height