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. A particular person weighs 192 pounds on the surface of the earth and the radius of the earth is 3900 miles. Determine the equation that relates weight, W, to the distance from the center of the earth, d, for this person.
Let W = the weight of the person. Let d = the distance of the person from the center of the earth. Because the radius of the earth is 3900 miles, d = 3900 miles.
The weight of the person varies inversely as the square of the distance the person is from the center of the earth. Therefore [tex]W = \frac{k}{d^{2}} [/tex] where k = constant.
When d = 3900 miles, W = 192 pounds. Therefore [tex] \frac{k}{3900^{2}} = 192[/tex] Multply each side by 3900². k = 2.9203 x 10⁹.
Answer: The equation is [tex]W = \frac{2.9203 \times 10^{9}}{d^{2}} [/tex]
