Solve for Person's Final Height After Jumping Off Bridge

[Illyasviel]

Homework Statement

Mass of person jumping off bridge = 60 kg
The bridge is 60m above the river
The cord only starts stretching after he falls 20m.
k = 50 N/m

Homework Equations

gravitational potential energy = mgh
elastic potential energy = (1/2)kx^2

The Attempt at a Solution

So this problem is asking how far below the bridge the person will fall before coming to a stop (before he bounces back up).

I did mgh = (1/2)kx^2 which is 36000J = (1/2)(50)(x^2) and got x = 38m. Can someone verify whether this is right? (As in did I set up the problem properly).

But my real question is for the second part. He bounces up and down a few times but eventually due to air friction he hangs at rest. At what height above the water is he then?

I'm not sure what I'm supposed to do exactly do to find this. Can someone offer hints?

 

[paul232]

I see your mistake at the first part. What is x and what is h?
X is not counted from the bridge. x is the distance from the neutral position of the spring. You use it like it s the distance from the bridge. You can either use the Conservation of Energy at h=40m ( when the spring starts stretching ) or the way you do it you must define your x differently. Your x there must be something like (distance from bridge) = 20+x where x is the distance from the neutral position of the spring. so the x you find must put it in this equation and distance= 20 + 38= 58meters from the bridge.

For the second part ( which is much much easier ) you need Only to think what happens when the man remains still. ΣFy=0