How fast must a roller coaster travel to safely make it though loops and over hills?

Here, you can choose how high up some steep downhill slope you want a roller coaster to start. The higher up you start the roller coaster, the more speed it can obtain as it rolls down. The goal is to choose the right starting height so that the roller coaster will safely make it to the very end of the track.

Click here to ride two other 'coasters, just for the fun of it.