SOLUTION: 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

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.)
----------
You have to use the distances from the Earth's center.
--> 90*(4000/4160)^2
===================
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.

RELATED QUESTIONS
Please, please, please, explain how you get the answer, I came up with 38% and I don't... (answered by longjonsilver)
Find the perimeter of the figure. (which i cannot draw) Its a square shape with a line... (answered by jim_thompson5910)
I know this a normal distribution problem, but I am really confused since it is... (answered by robertb)
You can afford a $1300 per month mortgage payment. You've found a 30-year loan at 7%... (answered by Theo)
Okay, so I'm really struggling on this question, and I was wondering if someone could... (answered by MathLover1,ikleyn)
this question has been driving me nuts for days!! it says to prove that:... (answered by AnlytcPhil)
The distance that a freely falling body falls varies directly as the square of the time... (answered by jim_thompson5910)
"Please help!!! I cannot figure out the answer to this question. I've tried different... (answered by MathLover1,stanbon)
A chocolate shop makes a dark chocolate that is 35% fat and a white chocolate that is 48% (answered by fractalier)

SOLUTION: I've being going round and round with this question, but cannot get it right. The weight of a body &#119908; varies inversely with the square of its distance from the center of

SOLUTION: 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