Final speed of an asteroid using escape speed

enchanteuse

1. The problem statement, all variables and given/known data

The escape speed from a very small asteroid is only 32 m/s. If you throw a rock away from the asteroid at a speed of 44 m/s, what will be its final speed?

2. Relevant equations

Ki + Ui = 1/2mv^2 + (-GMm/R) = 0 (for v<<c)

3. The attempt at a solution

I am unsure of how to do this problem because I don't have the masses or the radius. Any help would be greatly appreciated!

Delphi51

Isn't it just 44 - 32?

guitarman

It should be SQRT((44^2)-(32^2))

enchanteuse

Thank you! However, I would like to know the steps on how you got to the answer if possible...

Delphi51

The definition of escape speed is that it is the v that provides sufficient KE to take the object infinitely far away from the planet, where its velocity will then be zero.
So your object will have E = 1/2*m*44^2 - 1/2*m*32^2 energy leftover.
Put this back in E = 1/2*m*v^2 to see what the speed due to the leftover energy is.
No doubt guitarman has it right, but yes, you most definitely want to know why!

Thanks to guitarman for catching my mistake!