You stand on a spherical asteroid of uniform density whose mass is 3.0*10^16 kg and whose radius is 12 km (12*10^3 m). These are typical values for small asteroids, although some asteroids have been found to have much lower average density and are thought to be loose agglomerations of shattered rocks. The asteroid is rotating a bit faster than once per day, so that objects on the surface have a speed of 2 m/s, including you and a rock you are holding. You want to figure out how fast (relative to you) you have to throw the rock (in the direction of the asteroid's spin) so that it never comes back to the asteroid and ends up traveling at a speed of 12 m/s when it is very far away.

How fast (relative to you) do you have to throw the rock (in the direction of the asteroid's spin) so that it never comes back to the asteroid and ends up traveling at a speed of 12 m/s when it is very far away?

I've tried using Ki + Ui = Kf + Uf

but when i solved for the initial velocity, i got the answer incorrect.

Can anyone help me?

i may be wrong , but is the answer 19.85m/s ?