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For my year 12 maths c class, we're doing an assignment on bungee Jumping (Task sheet can be found by googling "maths c bungee jumping" first link will be the relative one (pdf file)).

For this assignment, the first question asks you to find a general formula for the maximum depth reached in the jump in terms of the jumpers mass and the natural length of the rope (where air resistance in negligent).

The relevant information given on the specifications of the rope being used is that: when a mass of 75kg is applied to the rope, the rope will stretch to a length twice its' equilibrium length (length without stretching).

The main difficulty I've encountered in answering this question has been attempting to find a general formula for k (Hooke's law) in terms of l (the natural length of the rope) and/or the mass.

After countless hours considering this problem, my best attempt at determining k has been to substitute the following into my equation for the velocity of the jumper for the section of the fall where tension plays a role: x(extension beyond natural length of rope)=l when m=75 and v=0, since when the velocity reaches 0, the mass will have reached its' lowest point.

Where g=acceleration due to gravity (9.81ms^-2)

1/2(v)^2=gx - k(x)^2/(2m) + (2lg)^.5

0=gl - k(l)^2/(2*75) + (2lg)^.5

And so on and so forth until the equation is rearranged to give k

Please, tell me if I'm using a valid method to determine k, and if not, please give me some hints on how I can, I've already read two physicsforums posts, posted by someone else, about this maths c assignment which were no help.