On the performance of Usain Bolt in the 100 metre sprint

摘要

Many university texts on Mechanics deal with the problem of the effect of theair drag force, using as example the slowing down of a parachute. Hardly no onediscuss what happens when the drag force is proportional to both $u$ and $u^2$.In this paper we deal with a real problem to illustrate the effect of bothterms in the speed of a runner: a theoretical model of the performance of the100 m world record sprint of Usain Bolt during the 2009 World Championships atBerlin is developed, assuming a drag force proportional to $u$ and to $u^2$.The resulting equation of motion is solved and fitted to the experimental dataobtained from the International Amateur of Athletics Federations that recordedBolt's position with a LAVEG (laser velocity guard) device. It is worth to notethat our model works only for short sprints.