at what altitude above the earth’s surface must they be for their weight to drop to 800 N?

Question

If a person weighs 882 N on the surface of the earth, at what altitude above the earth’s surface must they be for their weight to drop to 800 N? Explain.

Answer 1

mg = GMm/R²; g = GM/R²;

mg_h = GMm_h/(R + h)².

From here mg/mg_h = (R + h)²/R²; 882/800 = (R + h)²/R²; (R+ h)/R = √882/800) = 1.05;

h = 0.05R, where R is radius of Earth, R = 6365 km.

So h = 6365·0.05km= 318.25 km