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# the weight of an object............

The weight of an object varies inversely as the square of its distance from the center of the Earth. If an object at sea level (3978 mi from the center of the earth) weighs 220 lb, find its weight when it's 200 mi above the surface of the earth.

### 2 Answers by Expert Tutors

William S. | Experienced scientist, mathematician and instructor - WilliamExperienced scientist, mathematician and...
4.4 4.4 (10 lesson ratings) (10)
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No!  If we're going to be consistent we have to use 3,978 miles plus 200 miles (= 4178 miles) as the distance the object is from the center of the earth.  Remember, the problem states that the object is 200 miles above the surface of the earth, not the center of the earth.

w = 3,481,386,480 lb mi-2/(4178 mi)2

w = 3,481,386,480 lb mi-2/(17455684 mi2)

w = 199.441 lb

You are correct William, I didn't pay attention to that. Thanks for revising it.
Jose R. | Proficient and Patient Math TutorProficient and Patient Math Tutor
5.0 5.0 (6 lesson ratings) (6)
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varies inversely means y=k/x where k is the variation constant.
The weight of an object that's w
the square of it' distance that's d2
So we get w=k/d2..... Now it tells u that the object weighs 220lb and it's distance is 3978mi. So plug those numbers in the equation I had just written and solve for k.
220=k/(3978)2
k=3,481,386,480
So our new equation is w=3,481,386,480/d2
But now they ask to find the weight of the object when it's 200 miles above the surface earth.
So all we do is plug in 200 and solve for w.
w=3,481,386,480/(200)2
w=87,035 lbs (rounded to the nearest whole number)