On the performance of Usain Bolt in the 100 metre sprint

Abstract

Many university texts on Mechanics deal with the problem of the effect of the air drag force, using as example the slowing down of a parachute. Hardly no one discuss 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 both terms in the speed of a runner: a theoretical model of the performance of the 100 m world record sprint of Usain Bolt during the 2009 World Championships at Berlin 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 data obtained from the International Amateur of Athletics Federations that recorded Bolt's position with a LAVEG (laser velocity guard) device. It is worth to note that our model works only for short sprints.