When I studied mechanics at college, it wasn’t even called mechanics, but instead ‘applied maths’. Perhaps this is a better name for it? ‘Mechanics’ seems to suggest something too technical, hands-dirty, when in fact it is simply ‘practical maths’. Or it should be? Part of the reason some students react poorly to the subject seems to be that it is presented to them in exam papers and text-books, as a series of rather formulaic pseudo-problems, which bear little relation to the messiness of the actual world.
Whilst we may be stuck with such exam questions for the time being, the promotion and delivery of the subject is best done through actual real-world situations. The motivation gained from addressing such problems can easily be translated into exam familiarity but the reverse is not necessarily true – it is better to catch students’ enthusiasm early. This is why I tend to include real-world problems in mechanics (and statistics – the same principles seem to apply) when promoting the study of A level Mathematics.
We live in a golden age of real-world problems because of the ubiquity of online video clips. I would like to describe in some detail the development of one such problem into a versatile and engaging maths activity. In 2009 Felix Baumgartner performed what was at the time the highest free-fall parachute jump – literally from the edge of space. The short video that captures his descent (easily found online) is truly remarkable and can hardly fail to capture the attention of any student. Felix actually breaks the sound barrier after a mere 45 seconds of free-fall – the first human to do so – but only two minutes later has slowed to the ‘standard’ terminal velocity of around 120 mph. He opens his parachute after about 5 minutes of falling, and then lands normally. The graph of his descent can be plotted from information contained in the video clip, and a calculation which is fairly easily explained leads to the key problem being answered: how high above the Earth was Felix, when he jumped from his balloon?
As a teacher, it was the design and implementation of problems such as these that provided the greatest sense of satisfaction. It is time-consuming, of course, but ultimately hugely rewarding.