9 A bungee jumper, of mass 80 kg , is attached to one end of a light elastic cord, of natural length 16 metres and modulus of elasticity 784 N . The other end of the cord is attached to a horizontal platform, which is at a height of 65 metres above the ground. The bungee jumper steps off the platform at the point where the cord is attached and falls vertically. The bungee jumper can be modelled as a particle. Hooke's law can be assumed to apply throughout the motion and air resistance can be assumed to be negligible.

1. Find the length of the cord when the acceleration of the bungee jumper is zero.
2. The cord extends by \(x\) metres beyond its natural length before the bungee jumper first comes to rest.
   1. Show that \(x ^ { 2 } - 32 x - 512 = 0\).
   2. Find the distance above the ground at which the bungee jumper first comes to rest.