Trampolining is an Olympic sport that involves gymnastics tricks performed sometimes 4-5 meters above the ground using a trampoline. You can see a video of this here. A female gymnast of mass \(50~\mbox{kg}\) lands on a trampoline, stretching it downward. If after she bounces she reaches a height of \(5~\mbox{m}\) above the surface of the trampoline when it was fully stretched then how much energy in **joules** did the trampoline store?

**Details and assumptions**

- You may assume the gymnast goes straight up and down, is a point mass, and adds no extra energy this bounce by jumping.
- Take \(g\) to be \(9.8~\mbox{m/s}^2\).

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