Altitude of a Rocket Launched into Space

[tesla93]

The Problem:

A 4.60 kg rocket is launched directly upward from Earth at 9.00 km/s

What altitude above the Earth's surface does the rocket reach?


Relevant Equations:

v = √ (2GM/r)

The Attempt:

m = 4.60 kg
v = 9km/s = 9000m/s
G = 6.67 x 10^-11

9000^2 = 2(6.67^-11)(4.60)/r

r = 6.8 x 10-14m

I used that formula because it is for escape speed, which I think applies to this question, as it needs to be a certain height above the Earth to escape the pull and stay in orbit.

 

[ideasrule]

"M" is the mass of the Earth, not of the rocket. The mass of the rocket doesn't matter because in freefall, all objects accelerate at the same rate, regardless of mass.

 

[tesla93]

Oh alright that makes sense. Thank you!