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Question 1122062: I've being going round and round with this question, but cannot get it right.
The weight of a body 𝑤 varies inversely with the square of its distance from the center of Earth 𝑑. If a person weighs 90 pounds on the surface of Earth, what is the person’s weight 160 miles above the surface? (Assume that the radius of Earth is 4000 miles.)
In our text it says Inversely means multiply, and so I did,(yz=k):
90(160)^2=k
90(25600)=k
2304000=k
The part of the question that has me confused is when it talks about radius of the earth being 4000 miles.
I assumed it would be used as follows:
4000m/4000 = 2304000/4000
which gives an answer of: m = 576
This seems incorrect.
Any advice would be appreciated.
Found 2 solutions by Alan3354, Theo:
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! The weight of a body 𝑤 varies inversely with the square of its distance from the center of Earth 𝑑. If a person weighs 90 pounds on the surface of Earth, what is the person’s weight 160 miles above the surface? (Assume that the radius of Earth is 4000 miles.)
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You have to use the distances from the Earth's center.
--> 90*(4000/4160)^2
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It's a typical inverse square problem.
Applies to gravity, sound, light, etc.
If the distance is multiplied by x, the intensity is multiplied by 1/x^2
Answer by Theo(13342)  (Show Source):
You can put this solution on YOUR website! inverse proportion formula is y = k / x
when you say that the the weight of a person varies inversely with the square of the distance from the center of the earth, the formula becomes:
w = k / d^2
when w = 90 and d = 4000, the formula becomes 90 = k / 4000^2.
solve for k to get k = 90 * 4000^2 = 144 * 10^7.
when the person is 160 miles above the surface of the earth, the person is 160 + 4000 = 4160 miles from the center of the earth.
the formula then becomes y = k / d^2 which becomes y = 144 * 10^7 / 4160^2.
solve for y to get y = 83.21005917.
that should be your answer.
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