Calculating Escape Velocity for a Small Asteroid with Given Initial Velocity

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The discussion centers on calculating the final speed of a rock thrown from a small asteroid with an escape velocity of 28 m/s and an initial velocity of 39 m/s. The key equation referenced is the conservation of energy, which simplifies to a relationship involving kinetic and potential energy. The challenge arises from the lack of specific values for the asteroid's radius and mass, making it difficult to directly calculate the final velocity. Participants are encouraged to explore how escape velocity relates to the initial conditions provided. Ultimately, the problem highlights the need for additional information to solve for the final speed accurately.
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Homework Statement


The escape speed from a very small asteroid is only 28 m/s. If you throw a rock away from the asteroid at a speed of 39 m/s, what will be its final speed?
Vesc= 28m/s
Vi= 39 m/s

Homework Equations


Ks,f + Ke,f + Uf = Ks,i + Ke,i + Ui +W
Vi=sqrt(2GM/r)

The Attempt at a Solution



Well I know the first equation gets simplfied to
0=.5mv^2 + (-GM/r)
Vi=sqrt(2GM/r)

But I don't have radius or mass of my asteroid and I don't have any equations that incorporate the final velocity...

But I can't figure out how to
 
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How can you relate the asteroid's escape velocity to the values you're looking for?
 

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