Question

The weight of a person on or above the surface of the earth varies inversely as the square of the distance the person is from the center of the earth. If a person weighs 180 pounds on the surface of the earth and the radius of the earth is 3900 miles, what will the person weigh if he or she is 325 miles above the earth's surface? Round your answer to the nearest hundredth of a pound.
a.

154.77 lb
b.

153.77 lb
c.

152.87 lb
d.

153.37 lb

Answer 1

\(Weight = \dfrac{k}{d^{2}}\)

What to do with that?

Answer 2

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies inversely to }&\textit{something else}\\ \quad \\
\textit{something }&=\cfrac{{\color{red}{ \textit{some value }}}}{\textit{something else}}\\ \quad \\
y&=\cfrac{{\color{red}{ n}}}{x}
&&\implies y=\cfrac{{\color{red}{ n}}}{x}
\end{array}\) notice tkhunny line above

Answer 3

any thoughts?

Answer 4

no i dont get it at all...

Answer 5

one sec

Answer 6

the part I sorta find a bit misleading is
"If a person weighs 180 pounds on the surface of the earth"

since every person would more or less would be on the surface all the time anyway
unless one goes under in a cave

notwithstanding that one sec

Answer 7

yeah i got that so how do u set this up? i tried the 1st comment way but got wrong answer...

Answer 8

sorry got a bit criss-crossed with the wordings

Answer 9

\(\bf \begin{array}{cccllll}
\textit{something }&\textit{varies inversely to }&\textit{something else}\\ \quad \\
\textit{something }&=\cfrac{{\color{red}{ \textit{some value }}}}{\textit{something else}}\\ \quad \\
y&=\cfrac{{\color{red}{ k}}}{x}
&&\implies y=\cfrac{{\color{red}{ k}}}{x}
\end{array}
\\ \quad \\
weight(\textit{of person on surface})=\cfrac{{\color{red}{ k}}}{d(\textit{istance from center})^2}\implies w=\cfrac{{\color{red}{ k}}}{d^2}
\\ \quad \\
when\ w=180\qquad d=3900\implies 180=\cfrac{{\color{red}{ k}}}{3900^2}
\\ \quad \\
\textit{then, what is "w" when d = 325?}\)

Answer 10

bear in mind that
the distance used is from the center of the planet
the weight of a person is based on the "gravity pull" the planet has on the body over a distance

the idea being, the center of the planet is doing the gravity pulling
the farther up you go, the less the pull affects you
the pull in colloquial lingo is just "weight"

Answer 11

since the person would be 325 "above the earth's surface
and the earth has a radius of 3900 miles or

Answer 12

find "k" and then set "d" accordingly