Inverse Variation

IDontunderstand · #1 $Old$ 11-18-2008, 04:08 PM

The acceleration due to the earths gravitational atteraction varies inversely as the square of the the distance from the center of the earth. The acceleration is 32 feet per second per second at 4000 miles from the center. What is the acceleration in feet per second per second of a satlelite 8000 miles from earth?

I get the answer of 16 but am told the answer is 8

xy=K so 32(4000)=128000 then say x(8000)=128000 divide 128 by 8= 16

or if we think about is since 4000 is doubled so the other value has to be taken in half so that would be 16

Am I right or just totally wrong Thank you

skeeter · #2 $Old$ 11-18-2008, 04:32 PM

Quote:

Originally Posted by IDontunderstand $View Post$

The acceleration due to the earths gravitational atteraction varies inversely as the square of the the distance from the center of the earth. The acceleration is 32 feet per second per second at 4000 miles from the center. What is the acceleration in feet per second per second of a satlelite 8000 miles from earth?

let $R = 4000$ miles

$\frac{k}{R^2} = 32$

double $R$ ...

$\frac{k}{(2R)^2} = \frac{k}{4R^2} = \frac{1}{4} \cdot \frac{k}{R^2} = \frac{1}{4} \cdot 32 = 8$

IDontunderstand · #3 $Old$ 11-18-2008, 05:25 PM

Quote:

Originally Posted by skeeter $View Post$

let $R = 4000$ miles

$\frac{k}{R^2} = 32$

double $R$ ...

$\frac{k}{(2R)^2} = \frac{k}{4R^2} = \frac{1}{4} \cdot \frac{k}{R^2} = \frac{1}{4} \cdot 32 = 8$

So we say R so we dont have to write 4000 correct,so

$\frac{k}{x}=y$

that is our formula so I can replace x with R, and so y=32

Then I have to double R because 8000 is 2(4000) and square it because per sec per sec?

skeeter · #4 $Old$ 11-18-2008, 05:38 PM

Quote:

So we say R so we dont have to write 4000 correct,so

that is our formula so I can replace x with R, and so y=32

Then I have to double R because 8000 is 2(4000) and square it because per sec per sec?

I'm sorry, but this explanation/statement/question makes no sense.

look again at the original problem statement ...

The acceleration due to the earths gravitational attraction varies inversely as the square of the the distance from the center of the earth.

translating this statement into an equation ...

$a = \frac{k}{R^2}$ , where R is the distance.