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Physics question about BUNGEE JUMP

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Hi all,

I have stuck on a bungee question, the question is about this:

A bungee jumper of mass 60 kg jumps from a bridge 24m above the surface of the water. The rope is 12m long and is assumed to obey Hooke's law.

a) what should the spring constant of the rope be if the woman is just to reach the water?

no prob. with that

b) what is the speed of the jumper when she has fallen by 12m?

again, I solved it

C) what is the maximum speed attained by the jumper during her fall?

cant solve this, how do I find the maximum speed?? please help!!

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The maximum speed is attained when the net acceleration of the bungee jumper is zero (the acceleration due to gravity being balanced by that due to the restoring force of the stretched bungee cord). You know the acceleration due to gravity, and you can calculate the acceleration due to the extension of the bungee cord by Hooke's law, so you can find the extension at which the velocity is greatest. Remember that the sum of the potential, kinetic and elastic energy is constant. So you can find the maximum velocity by expressing the kinetic energy in terms of the potential energy and the elastic energy of the cord at that point.

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Start off by calculating the energy in the initial point, it's easy seeing as becauase there is no movement and the rope isn't currently being used, there is only potential energy. Once you have it calculate the energy of the jumper when it has reached the water hence making the potential energy 0. You have elastic and kinetic energy, get the elastic energy, and make it so elastic energy+kinetic energy= initial potential energy and solve for speed. Hope this helps.

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