Calculating Spring Compression for Escape Velocity from Spinning Asteroid

[clutch12]

Homework Statement

A package of mass 9 kg sits at the equator of an airless asteroid of mass 6.1 * 10^5 kg and radius 36 m, which is spinning so that a point on the equator is moving with speed 2 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 189 m/s. We have a large and powerful spring whose stiffness is 1.1*10^5 N/m. How much must we compress the spring?

Homework Equations

Kp,f = Kp,i + Ui + W

The Attempt at a Solution

Im kinda lost at how to attempt this problem so any help explaining me through the process would be great.

 

[Delphi51]

Looks like an energy conversion problem. You could write
initial energy = final energy
then put in expressions for the various kinds of energy it has. Don't forget the gravitational potential energy.

 

[clutch12]

Alright thanks imma work on this problem and see what i get as an answer