Question

On the surface of the earth the weight of an object is 200 lb. Determine the height of the

object above the surface of the earth, in miles, for the object to register a weight of 125
pounds.

Answer 1

The height of the object is 5007.4 miles.

Step-by-step explanation:

Given that,

Weight of object = 200 lb

We need to calculate the value of
`Gmm_(e)`

Using formula of gravitational force

`F=(Gmm_(e))/(r^2)`

Put the value into the formula

`200=(Gmm_(e))/((3958.756)^2)`

`200*(3958.756)^2=Gmm_(e)`

`Gmm_(e)=3.134*10^(9)`

We need to calculate the height of the object

Using formula of gravitational force

`F=(Gmm_(e))/(r^2)`

Put the value into the formula

`125=(200*(3958.756)^2)/(r^2)`

`r^2=(200*(3958.756)^2)/(125)`

`r^2=25074798.5`

`r=√(25074798.5)`

`r=5007.4\ miles`

Hence. The height of the object is 5007.4 miles.