From what height above the surface of the earth should an object be dropped to initially experience an acceleration of 0.54g?
(G = 6.67 × 10^-1¹ N ∙ m²/kg², M_earth = 5.97 × 10²⁴ kg, R_earth = 6.38 × 10⁶ m)

Question

Quizplus · Accepted Answer

The acceleration experienced by an object dropped from a height h above the surface of the Earth is given by:
a = GM/R^2
where G is the gravitational constant, M is the mass of the Earth, R is the radius of the Earth, and h is the height of the object above the surface of the Earth.

We are given that the initial acceleration experienced by the object is 0.54 g, where g is the acceleration due to gravity on the surface of the Earth (9.81 m/s^2). Therefore,
a = 0.54g = 0.54 × 9.81 m/s^2 = 5.301 m/s^2

Substituting the given values, we get:
5.301 = (6.67 × 10^-11 N∙m^2/kg^2)(5.97 × 10^24 kg)/(6.38 × 10^6 m + h)^2

Solving for h, we get:
h = 2,300 km

Therefore, the object should be dropped from a height of 2,300 km above the surface of the Earth to initially experience an acceleration of 0.54g.

From What Height Above the Surface of the Earth Should