and of course make sure the egg doesn't crack too...
Use a "C" motor. Yes, there's lots of different kinds of "C" motors, you're probably going to want to learn a bit about them so you can make an informed choice. If you're new to rockets, you may want to start at Wikipedia.
If you want to buy your own, check out Amazon
or go to Hobby Lobby or some such local store. I'll have some available in class at cost too (first come first served!) Here's a listing of local Hobby Lobby stores - but try searching for other model rocket stores too!
