Analysing Usain Bolt using GeoGebra/Document: Difference between revisions

The summer of 2012 has seen the culmination of the very successful London 2012 Olympic Games with the Jamaican sprinter, Usain Bolt, taking gold medals in the men’s sprint events. While we do not yet have official 10m split timings from the International Association of Athletics Federations (IAAF), there are now some postings of his 20m split times on the Internet: [http://speedendurance.com/2012/08/09/usain-bolt-20-meter-splits-london-2012-olympics/ http://speedendurance.com/2012/08/09/usain-bolt-20-meter-splits-london-2012-olympics/]. The technique for statistical analysis used here recognises that the displacement and velocity are both zero until the runner leaves the blocks. This does not happen just as the starting pistol is fired, but slightly later due to the athlete’s reaction time delay, RT. For Bolt in London 2012 this was estimated at 0.165 s. So if we try to fit a polynomial regression model to the time v distance data it should have (x-RT) as a double factor. So the trick is to divide the distance data values y by the factor (x-RT)², where x is the time data value, and then to fit a polynomial regression model, such as a cubic, to the resulting data points, ignoring the initial (RT,0) data point. This technique gives a good fit to the data.