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The weight of a body is inversely proportional to the square of the distance from the body to the center of Earth. Assuming an Earth radius of 4000 miles, a man who weighs 230 pounds on Earth's surface would weigh how much 20 miles above Earth? Round your answer to the nearest integer.

The weight at 20 miles above Earth's surface is _____ pounds.

Answer :

The weight at 20 miles above Earth's surface would be approximately 23,000,000 pounds.

To solve this problem let's first define the variables:

  • W₁ = Weight on Earth's surface = 230 pounds
  • R₁ = Radius of Earth (in miles) = 4000 miles
  • R₂ = Distance from the body to the center of Earth at 20 miles above the surface (in miles)

According to the given information weight is inversely proportional to the square of the distance. Therefore we can may be set up the following equation

[tex]W_{1} / W_2= (R_2^2) / (R_1^2)[/tex]

To find W₂ (the weight at 20 miles above Earth's surface) we can rearrange the equation as follows

[tex]W₂ = (W_1 * R_1^2) / R_1^2)[/tex]

Substituting the given values:

  • [tex]W_2 = (230 * 4000^2) / (20^2)[/tex]
  • [tex]W_2 = (230 * 16000000) / 400[/tex]
  • [tex]W_2 = 9200000000 / 400[/tex]
  • [tex]W_2 = 23000000[/tex]

Therefore, the weight at 20 miles above Earth's surface would be approximately 23,000,000 pounds.

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