Changing mass phenomena like the motion of a falling chain, the behaviour of a falling elastic bar or spring, and the motion of a bungee jumper surprise many a physicist. In this article we discuss the first phase of bungee jumping, when the bungee jumper falls, but the bungee rope is still slack. In instructional material this phase is often considered a free fall, but when the mass of the bungee rope is taken into account, the bungee jumper reaches acceleration greater than "g". This result is contrary to the usual experience with free falling objects and therefore hard to believe for many a person, even an experienced physicist. It is often a starting point for heated discussions about the quality of the experiments and the physics knowledge of the experimentalist, or it may even prompt complaints about the quality of current physics education. But experiments do reveal the truth and students can do them supported by information and communication technology (ICT) tools. We report on a research project done by secondary school students and use their work to discuss how measurements with sensors, video analysis of self-recorded high-speed video clips and computer modelling allow study of the physics of bungee jumping. (Contains 7 figures.)