Question

a police inspector in a jeep is chasing a pickpocket on a straight road. The jeep is going at its maximum speed v. the pickpocket rides on the motorcycle of a waiting friend when the jeep is at distance d away, and the motorcycle starts with a constant acceleration a. show that the pickpocket will be caught if v is greater and equal to √2ad. ​

Answer 1

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=  

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

​