What's Maria's weight?

Question

The weight of an object above the surface of the earth varies inversely with the square of the distance from the center of the earth. If Maria weighs 125 pounds when she is on the surface of the earth (3690) miles from the center), determine Maria's weight if she is at the top of Mount McKinley (3.8 miles from the surface of the earth).

Here was my work:

W = K/D²

125 = K/3690²

W = 1960200000/3.8²

That obviously gave me the wrong answer. Was I supposed to convert the 3.8 somehow?

Answer 1

Leah, I didn't take out a pencil. But thank you for your well posed question. But why if it's obviously wrong is it not obvious what the issue is?

1. I think that you calculated K wrong. (125 * 3690^2)
2. I think that Mt. McKinley is 3.8 miles from the surface not from the center but that might not be enough to detect the amount of error that you are finding.

Answer 2

Yes, the top of Mount McKinley is not 3.8 miles from the center of the earth, it is 3690 + 3.8 miles from the center of the earth.

By the way, good job checking whether your answer was reasonable or not. That is often the first step towards catching, and ultimately correcting, an error.

Answer 3

You changed variables

125 = K / 3690²

125 = K / 13616100

0.000009180 = K

W = 918 x 10^-6 / 14022²

Can you compute and answer?