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

Answer 1

Suppose the pickpocket is caught at a time t after motorcycle starts. The distance traveled by the motorcycle during this interval is

s=

2

1

at

2

...(1)

During this interval the jeep travels a distance

s + d = vt ...(2)

By (1) and (2),

2

1

at

2

+d=vt

or,

t=

a

v±

v

2

−2ad

The pickpocket will be caught if t is real and positive.

This will be possible if

v

2

≥2ador,v≥

2ad

Hence, the pick pocket will be caught if v

2

≥2ador,v≥

2ad

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