Energy considerations in solving a bungee jumper question

[Toranc3]

Homework Statement

A bungee cord is 30.0 m long and, when stretched a distance x, it exerts a restoring force of magnitude kx. Your father-in-law (mass 95 kg) stands on a platform 45.0 m above the ground, and one end of the cord is tied securely to his ankle and the other end to the platform. You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 m before the cord stops him. You had several bungee cords to select from, and you tested them by stretching them out, tying one end to a tree, and pulling on the other end with a force of 380 N.

When you do this, what distance will the bungee cord that you should select have stretched?

Homework Equations

F=kx

K+U=K+U

The Attempt at a Solution

In this sentence "You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 m before the cord stops him." Does it mean that his velocity is zero there? I am confused with this sentence.

Here is what I have but this is wrong.

K1+U1=K2+U2
my point 1 is when he is at the top, y=45m and point 2 is where he is at the bottom, y=41m.

mgy1=mgy2 +1/2k(x)^2
(95)(9.8)(45)=(95)(9.8)(41) + 1/2k(11)^2

What am I doing wrong?

 

[haruspex]

In this sentence "You have promised him that when he steps off the platform he will fall a maximum distance of only 41.0 m before the cord stops him." Does it mean that his velocity is zero there?

Yes

.
where he is at the bottom, y=41m.

When he has fallen 41m, what will be his height from the ground?

 

[Toranc3]

Yes
When he has fallen 41m, what will be his height from the ground?

Would it be 4m?

 

[haruspex]

Yes, so y=4m at that point.