Question

at what height will be a man's weight be half his weight on the surface of Earth?

Answer 1

The problem cannot be solved using the formula g'/g = 1-(2h/Re) as h/Re is not coming out to be very small. One needs to go back to the original derivation where:

g'/g = (Re/Re + h)^2

as g'=g/2

Re + h=√2Re

h={√2–1}Re

Re= 6400 Km

h=2651Km

This gives h around 2651 Km which is a significantly different from 1600 Km. While solving these problems one needs to identify whether approximated formula is applicable or not.

Hope this helps!!