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**1. The problem statement, all variables and given/known data**

The Royal Gorge bridge over the Arkansas River is 310 m above the river. A 60-kg bungee jumper has an elastic cord with an unstressed length of 50 m attached to her feet. Assume that, like an ideal spring, the cord is massless and provides a linear restoring force when stretched. The jumper leaps, and at at her lowest point she barely touches the water. After numerous ascents and descents, she comes to rest at a height h above the water. Model the jumper as a point particle and assume that any effects of air resistance are negligible.

**2. Relevant equations**

1/2kx^2 is the elastic potential

mgh is grav potential

1/2mv^2 is KE

**3. The attempt at a solution**

I set the river to be my zero potential height, so before the jumper goes, she has an initial gravitational potential of mgh where h is 310m. At the bottom, when she barely touches the water, she has an elastic potential of 1/2kx^2, where x is 310-50=260. So I solved for k. getting 5.392899 N/m

Now when she has oscillated a bit and has finally come to a stop, she has gravitational and elastic potential. So this is what I solved for:

[tex]mgh_{initial}=\frac{1}{2}k(h-260)^2 +mgh[/tex] The h in the left hand side of the eqn is 310, I tried to solve for h in the right hand side but I got back to zero as an answer. So am I setting up wrong?

Also I need to find the max velocity.