Alphymus

A man with mass $m$ jumps off of a high bridge with a bungee cord attached to his ankles. The man falls through a maximum distance $H$ at which point the bungee cord brings him to a momentary rest before he bounces back up. The bungee cord is perfectly elastic, obeying Hooke's force law with a spring constant k, and stretches from an original length of $L_0$ to a final length $L = L_0 + h$. The maximum tension in the Bungee cord is four times the weight of the man.
Find the maximum extension of the bungee cord $h$.

(A) $h = \frac 1 2 H$
(B) $h =\frac 1 4 H$
(C) $h = \frac 1 5 H$
(D) $h = \frac 2 5 H$
(E) $h = \frac 1 8 H$