We present a case study of the physical principles necessary to model the high altitude parachute jump made by Colonel Joseph Kittinger, USAF, in 1960, in order to determine the maximum speed attained and to calculate whether this speed was sufficient to exceed the speed of sound at that altitude. There is considerable discrepancy in the value of the maximum speed attained--614 miles per hour (mph) or 714 mph--in material available over the internet. Using a very simple physical model we are able to conclude that the lower figure is correct and that it is likely that Colonel Kittinger did not "break the sound barrier" during his descent. The wealth of audio-visual material and animations available makes this a particularly attractive case study to instruct students in elementary kinematics, approximation and physical modelling. (Contains 2 figures.)