Elmer Fudd wants to take out Bugs Bunny with a rocket launcher.  While the rabbit is running south, Elmer aims the rocket east, and times the launch so the rocket will collide with Bugs as he passes by.

However, Bugs is rather agile, and instead of being smeared by the rocket, he leaps onto it and hangs on for dear life.  Given the information provided below (invented by my Physics students, and yes, we recognize that some of these numbers are ridiculous, but hey, they're cartoon characters, right?), what will the velocity of the rocket (and Bugs) be after the collision?

Rocket Mass: 125 kg
Rocket Velocity: 300 m/s east

Bugs Bunny Mass: 15kg
Bugs Bunny Velocity: 25 m/s south