Describe the energy changes in the 4 stages of a bungee jump - at the top, in freefall, when the cord is stretching and at the bottom

There are 3 forms of energy during a bungee jump, kinetic (KE = 0.5mv^2), gravitational potential (GPE = mgh) and elastic potential (EPE = 0.5kx^2). Energy is conserved throughout, and it's assumed none is lost as heat due to air resistance. At the top the rope is slack, velocity = 0 and so all of the energy is in the form of gravitational potential. In freefall, the rope is still slack so EPE = 0. KE is increasing with the acceleration due to gravity and GPE is decreasing as height reduces. As the cord stretches EPE increases. KE will continue to rise briefly before falling as velocity could continue to increase if the acceleration due to gravity is initially greater than the acceleration from the bungee cord. GPE will continue to decrease as the height falls. Finally at the bottom GPE is at a minimum, KE = 0 and EPE is at a maximum.

The key thing throughout this problem is to take the variable out of each equation (v for KE, x for EPE and h for GPE) and thing about their magnitude at each point relative to the other points.