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 325 miles above the earth's surface? Round your answer to the nearest hundredth of a pound.

a.

154.77 lb

b.

153.77 lb

c.

152.87 lb

d.

153.37 lb

The answer is 153.37 lb

The weight (w) of a person on or above the surface of the earth varies inversely as the square of the distance (d²) the person is from the center of the earth:

w = k/r ²

w * d² = k

w1 * d1² = k

w2 * d2² = k

w1 * d1² = w2 * d2² = k

We know:

On the Earth:

w1 = 180 lb

d1 = 3900 mi

Above the Earth

w2 = ?

d2 = 3900 + 325 = 4225 mi (we must add the total distance from the center of the Earth).

w1 * d1² = w2 * d2²

w2 = w1 * d1² / d2²

w2 = 180 * 3900² / 4225²

w2 = 180 * (3900/4225) ²

w2 = 153.37 lb