Chapter 7.1, Problem 30E

To determine

To Find: The weight of the astronaut at $200$ miles above the sea level.

Answer to Problem 30E

  $190$ Pounds

Explanation of Solution

Given: The weight $w$ in pounds of an object varies inversely with the square of the distance $d$ of the object from the center of the Earth. At sea level ( $3978$ miles from the center of the Earth), an astronaut weighs $210$ pounds.

The equation formed by the given data is

  $w=\frac{a}{d^2}$

Put $d=3978,w=210$

  $\begin{array}{l}210=\frac{a}{{3978}^2}\\ a=3,323,141,640\end{array}$

Substitute $a=3,323,141,640$ in $w=\frac{a}{d^2}$

We get

  $w=\frac{3,323,141,640}{d^2}$

Now

When distance is $200$ miles above the sea level

i.e.

  $d=3978+200=4178$

Weight of the astronaut is

  $\begin{array}{l}w=\frac{3,323,141,640}{{4178}^2}\\ w=190\end{array}$

Hence, the weight of the astronaut is $190$ pounds.