If the physics and mathematics of bungee jumping are amongst your interests, you are, as they say, spoilt for choice. There are quite a number of readily accessible academic studies at your disposal. Might we suggest (in no particular order)…
• Understanding the physics of bungee jumping by A. Heck, P. Uylings, E. Kędzierska
• Bungee jump model with increased stretch-prediction accuracy
by J. W. Kockelman, M. Hubbard
• The Greater-Than-g Acceleration of a Bungee Jumper
by David Kagan and Alan Kott
• The Mechanics of Bungee Jumping
by D. R. H. Jones
Safety notes: Before embarking on any practical bungee-based experiments involving humans, it might be an idea to read this advice provided by the University of Maryland, US.
DANGER – IMPORTANT NOTE: Bungee cords are made of shock cords (elastomers) or from rubber. They DO NOT behave as linear springs. It would be dangerous to assume linearity of a real bungee jumping cord and make calculations on this basis.
Also see: Give ‘Em Enough Rope: Perception of Health and Safety Risks in Bungee Jumpers