Question

What is the relationship between force, work and energy experienced by a bungee jumper

Answer 1

For a Bungee Jumper, assuming the rope is not taut and is jumping in vacuum space, experiences a net force downwards (weight) , Energy experienced is \[\Delta Potential Energy lost \] = \[\Delta Kinetic Energy Gained\] , since force is downwards, and displacement is downwards, work done which is +ve= Force x displacement or = -\[\Delta Potential energy\]

If there is air, then add in the upward air resistance force into the net Force Equation,
for a taut rope since the jumper is no longer falling, there is upwards tension balanced with downwards weight, no net work done, all energy becomes elastic potential energy stored in the rope