Bungee jumper's lowest point using energy conservation

[jacksonpeeble]

Homework Statement

A 74.4-kg bungee jumper is standing on a tall platform (h0 = 46.6 m). The bungee cord has an unstrained length of L0 = 9.54 m and, when stretched, behaves like an ideal spring with a spring constant of k = 61.8 N/m. The jumper falls from rest, and it is assumed that the only forces acting on him are his weight and, for the latter part of the descent, the elastic force of the bungee cord. Determine how far the bungee jumper is from the water when he reaches the lowest point in his fall.

Homework Equations

mgh_f+.5ky²=mgh₀

The Attempt at a Solution

No idea, made several attempts with results close to 10.

 

[rock.freak667]

Try finding how much the cord extends when the person jumps.

 

[ehild]

How far is the jumper from his initial position when he is at the end of the maximally stretched cord?

ehild

 

[rolisp]

in my opinion you can divide the jump into 2 stages: 1) free falling (H of free falling = L= 9.54) 2) movement on y asis and in this stage you can set equation (using Newton's laws) weight force (m*g) - elastic force = m*a

 

[jacksonpeeble]

Thank you everyone for your advice - I am curious - in what order should I go about doing these operations.

For instance (without necessarily plugging in numbers for me, which I know would defeat the purpose of me actually learning the material), is there a step-by-step procedure that should be followed (and other equations)?

 

[rolisp]

in the first stage you can solve nothing but in second one you should use formula F(elastic) = k*(L-L0) and inferring from Newton's second law, that is any force = m*a we can get equation k*(L-L0) = m*a the acceleration is g=10m/s^2 because it is a vertical falling (i am not sure about my opinion but i think that..)
transforming the equation we can get that L = (m*g+k*L0)*k and a length between the water and the reachest point is H0-L