Momentum problem (motion of a system of particles?) Slingshot around moon

[demerdar]

NASA often uses the gravity of a planet to slingshot a probe on its way to a more distant planet. The interaction of the planet and the spacecraft is a collision in which the objects do not touch. How can the probe have its speed increased in this manner?

This problem confuses me, I want to use the conservation of momentum, but I can't really set it up, if I'm even going in the right direction. I could use some help with this problem. Thanks.

 

[Hootenanny]

Welcome to PF!

You are on the right lines with momentum, but you also need to use conservation of kinetic energy.

This page is very useful;
http://www.mathpages.com/home/kmath114.htm

-Hoot