How Much Faster Will a Rock Travel If Thrown at 30 m/s From an Asteroid?

[ohheytai]

The escape speed from a very small asteroid is only 22 m/s. If you throw a rock away from the asteroid at a speed of 30 m/s, what will be its final speed?

all i know is K+U = 0 i have no clue how to do this

 

[cepheid]

The escape velocity is defined in such a way that if an object has that initial velocity, then its initial kinetic energy will be just enough that the object's velocity will approach zero asymptotically as its distance increases, but will never quite reach zero. In other words, the velocity will be reduced to zero "at infinity." The reason for this definition is that it ensures that the object will definitely escape (because there is no finite distance at which the object will slow to a stop and then begin falling back).

In practice, you can take "at infinity" to mean "at a sufficiently large distance away."Therefore, if the initial kinetic energy is higher than this critical value, the object will actually come away with excess speed. In other words, if the depth of the potential well is equal to 1/2 * m * (22 m/s)^2 (so that this is the amount of energy that gets "used up" in escaping), and the object actually starts out with 1/2 *m * (30 m/s)^2, then how much excess energy (beyond that needed to escape) will the object come away with? Therefore, how much extra speed?