At a certain height above the earth's surface, the acceleration due to gravity is 4% of its value at the surface of the earth. Determine the height.

Explanation

Acceleration due to gravity at a height, h=4% of g.
Radius of earth, R=6400 K.M=`6.4xx10^(6)` m.
`:.g_h=(4)/(100)g` But `g_h=(g*R^2)/(1+(h)/(R ))^2`
`:.(4)/(100)g=(g)/(1+h/R^2) implies (1+(h)/(R ))^2=(100)/(4)`
Take roots on both sides then, `1+(h)/(R )=(10)/(2)`
`=5 implies 1+(h)/(R )=5 implies (h)/(R )=5-1=4`
`:. h=4R=6400xx4=25,600` k.m.