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 150 miles above the earth's surface? Round
Your answer to the nearest hundredth of a pound.
A) 166.91 lb
B) 166.41 lb
C) 167.31 lb
D) 168.31 lb

Question

Quizplus · Accepted Answer

The weight varies inversely as the square of the distance from the center of the Earth. The formula for weight at a distance $r$ from the center is $W = \frac{k}{r^2}$, where $k$ is a constant. At the surface, $r = 3900$ miles, so $180 = \frac{k}{3900^2}$. To find the weight 150 miles above the surface, $r = 4050$ miles. Using the inverse square law, the weight at 4050 miles from the center is calculated and rounded to the nearest hundredth, resulting in 166.91 pounds.

The Weight of a Person on or Above the Surface