Launch Package from Spinning Asteroid: Calculating Required Spring Compression

[fball558]

here is the problem
A package of mass 6 kg sits at the equator of an airless asteroid of mass 5.7e5 kg and radius 41 m, which is spinning so that a point on the equator is moving with speed 4 m/s. We want to launch the package in such a way that it will never come back, and when it is very far from the asteroid it will be traveling with speed 230 m/s. We have a large and powerful spring whose stiffness is 1.4e5 N/m. How much must we compress the spring?

not really sure where to start but what i tried was finding the escape velocity of the box by using sqrt(2GM/r) where G is the gravitation attraction between the two masses. then try to find how much work would need to be done to make the box move that fast and relate that work to the spring compression. but got the wrong answer. any help would be great.

 

[fball558]

never mind found it out. just had to assume that "far away" means no patential energy. it is traveling at 230 so find only kenetic. them use potential energy equation of spring 1/2ks^2 solve for s (spring stretch) and that is your answer. ends up being something like 1.5 meter or 1.05 forget what it was.