Bungee Jump Physics: Solving for Maximum Fall Length and Spring Constant

[ScienceMan123]

Ok so I'm trying to find the maximum length of fall before the bungee brings the jumper to a stop? So I've chosen a few arbitrary starting heights: 50m, 55m, 60m and a few arbitrary bungee spring constants: 25 N/m, 30 N/m, 35 N/m.

How would I go about in approaching this problem? I think this problem has something to do with Hook's Law and Elastic PE but I need some more help.

Thanks.

 

[JHamm]

I would start by considering that a change in kinetic energy is equal to the net work done on an object, the work done by gravity is just $mg\triangle h$ , what is the work done by the bungee?