## Problem involving Hooke's Law

Please help with the problem below if you can. I've attempted using $T=(\lambda x )/l$ but that doesn't seem to help.

A bungee jumper of mass m kg falls vertically from rest from a high bridge. One end of an elastic rope is attached to the jumper, the other end to the bridge at the point where the jumper commences her fall. The natural length of the rope is $l$ metres and the modulus of elasticity is 12 mg newtons.

At the moment when the jumper is brought instantaneously to rest by the rope, the extension of the rope is $a$ metres.

(a) Neglecting the effect of air resistance, use conservation of energy to show that the extension satisfies

$6a^2 - la - l^2 = 0$.

(b) Hence find, in terms of $l$, the distance the jumper falls before first coming instantaneously to rest.