Trampoline physics

I sit down in the center of a trampoline and the surface sinks down by a distance of 10 cm when I reach equilibrium. How far above the ground in m must the trampoline be placed so that if I jump onto the trampoline from a height of 3 m above the surface of the trampoline I won't hit the ground?

Details and assumptions

  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
  • I have a mass of 80 kg.
  • Model the trampoline as an ideal spring.

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