How high does a rocket have to go above the earth's surface until its weight is 0.4 t

[ahsanmhamid]

how high does a rocket have to go above the Earth's surface until its weight is 0.4 times its weight on the Earth's surface ? The radius of the Earth is 6.37 * 10 ^ 6m and the acceleration of gravity is 9.8 m/s^2. Answer in units of km.

what i got so far, i need help proceeding:

Applying the inverse-square law:

Final weight = 0.4 g = (1/2.5) g

The square root of 2.5 = 1.581

im stuck here, thanks :)

 

[arildno]

??

Wherever have used or set up the inverse square law?

 

[Mentz114]

weight on surface = G*m*M/radius^2

0.4*weight on surface = G*m*M/x^2

Solve for x.