From what height (in kilometers) off the surface of Earth should an object be dropped to initially experience an acceleration of 0.54 g?

r = 8675867.3 m above the earth's surface

Explanation:

let M be the mass of earth, g be the acceleration of gravity and r be the distance of the object above the surface of the earth.

the acceleration of gravity is given by:

g = GM / (r^2)

then

r^2 = GM/g

r = / sqrt{GM/g}

= / sqrt{ (6.67*10^-11) (5.972*10^24) / (0.54*9.8) }

= 8675867.3 m

Therefore, for object ot experience an acceleration of 0.54g it should be dropped at a height of 8675867.3 meters above the surface of the earth.