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A police inspector in a jeepis chasing a...

A police inspector in a jeepis chasing a pickpocket on a straightroad. The jeep is going at its maximum speed v (assumed uniform). The pickpocket rides on the motorcycle of a waiting friend when the jeepis at a distance 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 it `vgesqrt(2ad)`.

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Suppose the pickpocket is caught at a time t after the motorcycle starts.The distance travelled by the motorcycle during this interval is
.
`s=1/2 at^2` ...........i.
During this interval the jeep travels a distance
`s+d=vt.` ............ii
By i. and ii.
`1/2 at^2-vt+d=0`
`or , t=(v+-(sqrt(v^2-2ad)/a`
Thie pickpocket will becaught if t is real and positive.
This will be possible if
`v^2ge2ad or, vgesqrt(2ad)`
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