Question

A 100 kg. man decides to go bungee jumping off a bridge. The bungee cord has a relaxed length of 10.0 m, and acts as a perfect spring with a stiffness constant of 80 N/m. What is the maximum distance below the bridge that he will reach? (he will fall 10.0 m. before the bungee cord even starts to stretch)

Answer 1

change in potential energy due to fall
= m g (10+x)

storage of potential energy in spring = (1/2) k x^2
so

(1/2) k x^2 = m g (10 + x)

you have everything, solve quadratic
for x then:
distance below bridge = 10 + x