Final speed of an asteroid using escape speed

AI Thread Summary
The escape speed from a small asteroid is 32 m/s, and a rock thrown at 44 m/s will have a final speed determined by its kinetic energy. The discussion highlights that the leftover energy after accounting for escape speed can be calculated using the equation E = 1/2*m*(44^2) - 1/2*m*(32^2). This leftover energy can then be used to find the final speed by substituting back into the kinetic energy equation. Understanding the concept of escape speed is crucial for solving the problem accurately.
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Homework Statement



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?

Homework Equations



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

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!
 
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Isn't it just 44 - 32?
 
It should be SQRT((44^2)-(32^2))
 
Thank you! However, I would like to know the steps on how you got to the answer if possible...
 
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!
 

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