Simple Harmonic Motion - bungee jumping

[lucamacc]

Homework Statement

A woman bungee-jumper of mass 50 kg is attached to an elastic rope of natural length 15 m. The rope behaves like a spring of spring constant k = 220 N/m. The other end of the spring is attached to a high bridge. The woman jumps from the bridge.

a) Determine how far below the bridge she falls, before she instantaneously comes to rest.

Homework Equations

Fe = -kx, Fg= m*g... Fg=Fe, -kx=m*g
OR
1/2kx^2=mgh

The Attempt at a Solution

Okay, so this is a question that appears in the Tsokos book and although I am aware of the solution and how to acquire it (through the use of the conservation of energy; equating the potential energy and elastic energy) by using the formula above, I would like to know why the task cannot be solved through the conventional equating of forces. Since the woman is in free fall, the only other force that could cause her to stop is the restoring force of elastic rope, hence the formula above: Fg=Fe. Through using this formula, however I have gotten that x=17.2 m and the answer seems to be 27.2 m and I do not know why I cannot solve it through equations of force.

Please, help.

Thanks.

 

[Nathanael]

By equating the weight of the bungee jumper with the restoring force, you are creating the condition that the acceleration is zero.

In this problem you are not interested in when the acceleration is zero, you are interested in when the velocity is zero.