The weight of a body varies inversely as the square of its distance from the center of the Earth. If the radius of the Earth is 4000 miles, how much would a 200-pound man weigh 1000 miles above the surface of the Earth?

Question

15-02-2024
Mathematics

College

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The weight of a body varies inversely as the square of its distance from the center of the Earth. If the radius of the Earth is 4000 miles, how much would a 200-pound man weigh 1000 miles above the surface of the Earth?

Answer :

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Final answer:

The weight of a body varies inversely as the square of its distance from the center of the earth. To find out how much a 200-pound man would weigh 1000 miles above the surface of the earth, we can set up a proportion using the inverse variation equation.

Explanation:

The weight of a body varies inversely as the square of its distance from the center of the earth. This means that as the distance from the center of the earth increases, the weight of the body decreases. The equation for inverse variation is y = k/x^2, where y represents the weight of the body, x represents the distance from the center of the earth, and k is a constant.

To find out how much a 200-pound man would weigh 1000 miles above the surface of the earth, we can set up a proportion using the inverse variation equation. Let's assume the man weighs y pounds when he is 1000 miles above the surface of the earth:

y/200 = (4000/(4000+1000))^2

Solving for y, we get the weight of the man when he is 1000 miles above the surface of the earth.

Learn more about Inverse variation here:

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