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The weight of an object varies inversely as the square of the distance

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The weight of an object varies inversely as the square of the distance [#permalink]

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The weight of an object varies inversely as the square of the distance from the center of the earth. At Sea Level (6,400 km from the center of the earth), an astronaut weighs 100 lbs. How far above the Earth must the astronaut be in order to weigh 64 lb?

I am using the Variation Equation: yz = k as the object varies "inversely"

The correct answer is 1,600 km but I can't seem to get there.

Can someone shed some light on this one?

Thank you
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Re: The weight of an object varies inversely as the square of the distance [#permalink]

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New post 05 Jan 2018, 12:25
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sullivan88 wrote:
The weight of an object varies inversely as the square of the distance from the center of the earth. At Sea Level (6,400 km from the center of the earth), an astronaut weighs 100 lbs. How far above the Earth must the astronaut be in order to weigh 64 lb?

I am using the Variation Equation: yz = k as the object varies "inversely"

The correct answer is 1,600 km but I can't seem to get there.

Can someone shed some light on this one?

Thank you


The weight of an object varies inversely as the square of the distance from the center of the earth:

\(weight = \frac{k}{distance^2}\), where k is some constant.


\(100= \frac{k}{6,400^2}\) --> \(k=6,400^2*100\).

\(64=\frac{6,400^2*100}{x^2}\) --> \(x = \sqrt{\frac{6,400^2*100}{64}}=\frac{6,400*10}{8}=8,000\) from the center of the earth.

The distance from the Earth (sea level) = \(8,000 - 6,400 = 1,600\).
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Re: The weight of an object varies inversely as the square of the distance [#permalink]

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New post 05 Jan 2018, 12:27
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Bunuel wrote:
sullivan88 wrote:
The weight of an object varies inversely as the square of the distance from the center of the earth. At Sea Level (6,400 km from the center of the earth), an astronaut weighs 100 lbs. How far above the Earth must the astronaut be in order to weigh 64 lb?

I am using the Variation Equation: yz = k as the object varies "inversely"

The correct answer is 1,600 km but I can't seem to get there.

Can someone shed some light on this one?

Thank you


The weight of an object varies inversely as the square of the distance from the center of the earth:

\(weight = \frac{k}{distance^2}\), where k is some constant.


\(100= \frac{k}{6,400^2}\) --> \(k=6,400^2*100\).

\(64=\frac{6,400^2*100}{x^2}\) --> \(x = \sqrt{\frac{6,400^2*100}{64}}=\frac{6,400*10}{8}=8,000\) from the center of the earth.

The distance from the Earth (sea level) = \(8,000 - 6,400 = 1,600\).


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New to the Math Forum?
Please read this: Ultimate GMAT Quantitative Megathread | All You Need for Quant | PLEASE READ AND FOLLOW: 12 Rules for Posting!!!

Resources:
GMAT Math Book | Triangles | Polygons | Coordinate Geometry | Factorials | Circles | Number Theory | Remainders; 8. Overlapping Sets | PDF of Math Book; 10. Remainders | GMAT Prep Software Analysis | SEVEN SAMURAI OF 2012 (BEST DISCUSSIONS) | Tricky questions from previous years.

Collection of Questions:
PS: 1. Tough and Tricky questions; 2. Hard questions; 3. Hard questions part 2; 4. Standard deviation; 5. Tough Problem Solving Questions With Solutions; 6. Probability and Combinations Questions With Solutions; 7 Tough and tricky exponents and roots questions; 8 12 Easy Pieces (or not?); 9 Bakers' Dozen; 10 Algebra set. ,11 Mixed Questions, 12 Fresh Meat

DS: 1. DS tough questions; 2. DS tough questions part 2; 3. DS tough questions part 3; 4. DS Standard deviation; 5. Inequalities; 6. 700+ GMAT Data Sufficiency Questions With Explanations; 7 Tough and tricky exponents and roots questions; 8 The Discreet Charm of the DS; 9 Devil's Dozen!!!; 10 Number Properties set., 11 New DS set.


What are GMAT Club Tests?
Extra-hard Quant Tests with Brilliant Analytics

Re: The weight of an object varies inversely as the square of the distance   [#permalink] 05 Jan 2018, 12:27
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