It's not exactly the Olympics, but this "world record" trampoline slam dunk is certainly entertaining to watch -- especially with the exciting and dramatic commentary. There's a lot of physics here, but let's focus in particular on how energy principles make such a prodigious leap possible. Now obviously, without a trampoline, the highest most people can leap off the ground is only a foot or two. When a person jumps they contract and extend their muscles, resulting in a push off of the ground. The energy for muscle contractions ultimately comes from chemical reactions in the body that convert stored chemical potential energy into kinetic energy of the muscles, and subsequently of the jump. However, not all of that chemical energy is successfully converted into kinetic energy. Some is dissipated as heat, and a significant amount is lost into the ground.
Enter the trampoline. The beauty of the trampoline is that it acts as a highly elastic object. An elastic object (like a spring or a bouncy ball) is able to store energy in the form of elastic potential energy. This elastic energy is not lost into the surroundings, and can easily be reconverted into kinetic energy. That's why you can jump so high on the trampoline. Unlike with the ground, each time you impact the trampoline you get most of your kinetic energy back on the rebound. Therefore, if you keep converting chemical potential energy into kinetic energy by pushing off on each successive landing, you can get some impressively high bounces going. (Don't worry. You'll replenish this energy later when you eat something.) Once you have sufficient kinetic energy, all it takes is a slight change of trajectory and you'll be stuffing a basketball through a hoop. Just be careful on that final landing!
Adam Weiner is the author of Don't Try This at Home! The Physics of Hollywood Movies.