Question

A police inspector in a jeep is chasing a pickpocket an a straight road. The jeep going at its maximum speed v (assumed uniform). The pickpocket rides on the motor-cycle of a waiting friend when the jeep is at a distance d away, and the motorcycle starts with a constant acceleration a. The pick pocket will be caught if

• A. $v\ge \sqrt{2ad}$
• B. $v^2\ge \sqrt{2ad}$
• C. $v\ge \sqrt{3ad}$
• D. $v\ge \sqrt{2a{d}^2}$

Answer 1

Answer: (A)

$v\ge \sqrt{2ad}$

Answer is A.
Suppose the pickpocket is caught at a time t after motorcycle starts. The distance traveled by the motorcycle during this interval is
$s=\frac{1}{2}a{t}^2$ ...(1)
During this interval the jeep travels a distance
s + d = vt ...(2)
By (1) and (2),
$\frac{1}{2}a{t}^2+d=vt$
or,
$t=\frac{v\pm \sqrt{v^2-2ad}}{a}$
The pickpocket will be caught if t is real and positive.
This will be possible if
$v^2\ge 2ador,v\ge \sqrt{2ad}$
Hence, the pick pocket will be caught if $v^2\ge 2ador,v\ge \sqrt{2ad}$.