Bungee jumping

Classical Mechanics Level 5

A bungee jumper jumps from a bridge with a \(3~\mbox{m}\) long bungee cord. Once the cord starts to stretch, it acts like an ideal spring with coefficient of elasticity \(k = 100~\mbox{N/m}\). What should be the minimum height of the bridge in m so that this jump is safe for the jumper?

Details and assumptions

  • The jumper has a mass of \(80~\mbox{kg}\).
  • The acceleration of gravity is \(-9.8~\mbox{m/s}^2\).
  • There are at least two ways to solve this problem.
  • Treat the jumper as a point mass at the end of the cord.

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