Question

The gravitational force, F, between an object and the Earth is inversely proportional to the square of the distance from the object and the center of the Earth. If anastronaut weighs 215 pounds on the surface of the Earth, what will this astronaut weigh 2650 miles above the Earth? Assume that the radius of the Earth is 4000miles. Round your answer to one decimal place if necessary

Answer 1

Given:

F is inversely proportional to the square of the distance means that

$F=\frac{k}{d^2}$

So the value of "k" is:

$\begin{gathered} 215=\frac{k}{4000^2} \\ k=215\times(4000)^2 \\ k=3440000000 \end{gathered}$

Weigh in 2650 mile above

$\begin{gathered} F=\frac{k}{d^2} \\ F=\frac{3440000000}{(2650)^2} \\ F=\frac{3440000000}{7022500} \\ F=489.85\text{ pound} \end{gathered}$