Question

A police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v (assume it to be uniform). The pickpocket rides on the motorcycle of a waiting friend. When the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. Show that the pickpocket will be caught if $v\ge \sqrt{2ad}$.

Answer 1

As per the question, $vt=d+\frac{1}{2}a{t}^2\Rightarrow a{t}^2-2vt+2d=0\Rightarrow t=\frac{2v\pm \sqrt{4v^2-8ad}}{2a}$
For real roots $4v^2-8ad\ge 0\Rightarrow v\ge \sqrt{2ad}$