Question

The weight w (in pounds) of an object varies inversely with the square of the distance d (in miles) of the object from the center of Earth. At sea level (3978 miles from the center of the Earth), an astronaut weighs 210 pounds. How much does the astronaut weigh 200 miles above sea level?

Answer 1

Answer: 190 pounds .

Step-by-step explanation:

Given : The weight w (in pounds) of an object varies inversely with the square of the distance d (in miles) of the object from the center of Earth.

$w\ \alpha\ \dfrac{1}{d^2}\\\\ w=\dfrac{k}{d^2}$ , where k is a constant.   (1)

At sea level (3978 miles from the center of the Earth), an astronaut weighs 210 pounds.

Put w= 210 and d= 3978  in (1).

$210=\dfrac{k}{(3978)^2}\\\\ k= (3978)^2\times210=3323141640$

200 miles above sea level d= 3978 + 200=4178 miles

Now put d= 4178 and k= 3323141640 in (1)

$w=\dfrac{3323141640}{4178^2}=190.37\approx190$

Hence, the astronaut weighs 190 pounds .