Question

The law of gravity states that the weight w of an object varies inversely as the square of the distance from the center of the earth. If the weight of an object is 3 kg when the distance from the center of the earth is 6000 km, find the distance to the center of the earth when the weight of an object is 10 kg. (Round the solution to the nearest whole kilometer.)
The only thing I know is that it is not 1800

Answer 1

So you should know what they're talking about is this equation right here:
\[Weight=Gravitational Constant*\frac{ Mass_1*Mass_2 }{ distance^2 }\]

Or maybe better written as:

\[F=G\frac{ M_1M_2 }{ r^2 }\]

Now you're given the mass and distance, but you're still missing a few things that you'll need to look up:

The mass of the earth and the gravitational constant.

From here try to guess and figure it out and I'll help guide you, what do you think comes next?

Answer 2

I've never seen that equation before O.o

Answer 3

I don't even know, I'm so confused @Kainui

Answer 4

I think they want you to use
varies inversely as the square of the distance

w = k/d^2

Normally, (see http://www.regentsprep.org/Regents/math/algtrig/ATE7/Inverse%20Variation.htm
you use inverse variation w= k/d but in this case, we use d^2

Answer 5

the idea is to find k from the info given:
w= 3kg, d= 6000 km
3 = k/6000^2
k= 3*6000^2

now find d when w=10
10 = k/d^2
10=3*6000^2/d^2

can you solve for d ?

Answer 6

3286.34?

Answer 7

let's see
10=3*6000^2/d^2
d^2 = 3/10 * 6000^2
d= sqrt(3/10) * 6000
d= 3286.34

yes

Answer 8

Yay.!