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A police party is moving in a jeep at a ...

A police party is moving in a jeep at a constant speed v. They saw a thief at a distance x on a motorcycle which is at rest. The moment the police saw the thief, the thief started at constant acceleration a. Which of the following relations is true if the police is able to catch the thief?

A

`V^(2) lt alphaX`

B

`V^(2) lt 2alphaX`

C

`V^(2) gt 2alphaX`

D

`V^(2) = alphaX`

Text Solution

Verified by Experts

The correct Answer is:
C
Distance travelled by the police party in .t. sec. is vt.
Distance travelled by thief `x + (1)/(2) prop t^(2)`
`rArr x + (1)/(2) prop t^(2) le vt " " rArr (alphat^(2))/(2) - vt + x = 0`
`alphat^(2) -2vt + 2x = 0 rArr t = 2v pm sqrt(4v^(2)- 8alphax)`
`4v^(2) gt 8alaphx, v^(2) gt 2alphax`
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