Physics
posted by Amanda on .
At what altitude above the Earth's surface would your weight be threefourths of what it is at the Earth's surface? Assume re = 6.371 10^3 km.

Based on Newton's law of universal gravitation,
F=GMm/r²
which means that the weight would be inversely proportional to the square of the distance from the centre of the Earth.
If H is the altitude when the weight becomes 3/4 of what's on the surface, then
(re/(re+H))^2=3/4
Solve for H. 
Solved out for H:
(6371/sqrt(3/4))  6371 = H
for other fractions just plug in where 3/4's is.
Hope this helps!