How Far Must a Rocket Travel from Earth to Weigh 1/100th of Its Surface Weight?

[Stratosphere]

Homework Statement

How high above the surface of the Earth should a rocket be
in order to have 1/100 of its normal weight? Express your answer
in units of Earth radii.

Homework Equations

F=GMm/r²
F=mg

The Attempt at a Solution

r = √(( 6.67 x 〖10〗^(-11) x 5.97 x 〖10〗^24 )/0.098)
then divide by 6.37*10⁶

I asked for help from one of my friends and he emailed me this but I think he might have messed somthing up. I keep getting a really big number.

I also know the answer its 9 radii but i don't understand how to get that answer.

 

[mgb_phys]

You don't need to use the actual mass of the Earth or the value of G.

You know that the weight is F = GMm/r^2
You know 'GMm' doesn't change,
So all you are asking is what do you have to do to 'r' to make 'r^2' 1/100 as big

ps. Careful with the final answer, r is from the centre of the Earth but the question asks for height above surface.

 

[Stratosphere]

So i have to make r^2=1/10 of r^2?

 

[mgb_phys]

yes - it migth help to label them r_initial and r_final to avoid confusing yourself !

 

[Stratosphere]

so how do i do that i tried r^2/10 its not right.

 

[Stratosphere]

i think i got it, so I did r*10 then subtract 1 to get distance from Earth's surface not its center. Thnx for the help.

 

[mgb_phys]

More formally you would write
r_i² = 100 r_f²

Take square root of both sides, it also helps to know that sqrt(ab) = sqrt(a) * sqrt(b)