2006 VCAA Spring Question

[Shark 774]

A student, Sam, of mass 70 kg, is bungee jumping from a platform at the top of a tower. He reaches
the top of the tower by being towed up a slide of length 30. The friction between Sam and the slide provides a constant force of 300 N that opposes the motion. The total work done in dragging Sam up the slide to the top of the tower is 22 720 J. At the top of the tower Samís potential energy was greater by 13720J than it was on the ground. The height at the top it 19.6m. The natural length of the bungee cord is 10 m. Sam stops falling and fi rst comes to rest momentarily when the length of the bungee cord is 18 m. What is it the spring constant of the bungee cord?

See here: http://www.vcaa.vic.edu.au/vce/studies/physics/pastexams/2006/physics1w06.pdf

I tried to use F = kx, where F = ma. But VCAA says this is wrong because you are assuming that the gravitational force at the bottom is equal to the force in the spring. What's wrong with assuming this? (they said to use mgh = 0.5k(x^2))