Problema Solution
The weight of an object varies inversely as the second power of the distance from the center of the Earth. The radius of the Earth is approximately 4000 miles. If a person weighs 160 pounds on Earth's surface, what would this individual weigh 8000 miles above the surface of Earth?
Answer provided by our tutors
The weight (W) of an object on earth varies inversely as the second power of the distance (d) from the center of the Earth. This relationship can be expressed as:
W= k/d^2, where k is the constant of variation
To find the value of k, we'll substitute the given values of W = 160 lbs and d = 4000 miles into the last equation:
160 = k/(4000^2)
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k = 2.56*10^9
Our formula becomes:
W = 2.56*10^9/d^2
Substitute d = 4,000 + 8,000 = 12,000 mi
W = 2.56*10^9/12000^2
W = 2.56*10^3/12^2
W = 17.78 lbs
8000 miles above the surface of Earth the individual will weighed 17.78 lbs.