Answer
Weight would be 199.899 pounds at 1 mile above the surface of the earth
Work Step by Step
The weight (W) of a body varies inversely with the square of its distance(D) from the center of Earth.
=>$ W= \frac{k}{D^2}$
Radius of earth = 3960 miles
W = 200 pounds at surface that is D = 3960 miles
Putting the values in equation we get
$200 = \frac{k}{3960^2}$
=> $k = 200*3960^2$
To find weight at height of 1 mile, or D=3961 miles
=>$ W = \frac{k}{3961^2}$
=> $ W = 200* \frac{3960^2}{3961^2} = 200(\frac{3961-1}{3961})^2 = 200(1-\frac{1}{3961})^2$
Using approximation $(1+x)^n = 1+n$ when x<< 1
$W = 200- \frac{200*2}{3961} = 199.899\ pounds $
