Question

How many kilometers would you have to go above the surface of the earth for your weight to decrease to 30 % of what it was at the surface?

Express your answer using 2 sig figs

Answer 1

Weight is the gravitational force exerted by Earth on us

is M is the mass of earth, R is the radius of Earth, m is the person's mass,then at surface

F = GMm/R²---------(1)

Let the weight (force, F') be 30% of what it was, at height 'h'

F' = 0.3*F

F' = GMm/(R+h)²--------(2)

then, from 1 and 2

0.3*GMm/R² = GMM/(R+h)²

taking square root we get,

R = ±sqrt(0.3)*(R+h)

ignoring -ve as distance cannot be negative

R = 0.55(R+h)

h = R*(1-0.55)/0.55

since, R = 6378.1 km

h = 5266.66 km