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A police van moving on a highway with a ...

A police van moving on a highway with a speed of `30 km h^(-1)` Fires a bullet at a thief's car speeding away in a same direction with a speed of `192 km h^(-1)`. If the muzzle speed of the buller is `150 m s^(-1)`, with what speed does the bullet hit thief's car? .
.

A

`105 ms^(-1)`

B

`205 ms^(-1)`

C

`305 ms ^(-1)`

D

`405 ms ^(-1)`

Text Solution

Verified by Experts

The correct Answer is:
A
Speed of the thief.s car with respect to ground is
`V_("TG") = 192 " km h"^(-1)`
Speed ofpolice van with respect to ground is `v_(PG) = 30 " km h"^(-1)`
`V_(BP) = 150 " ms"^(-1) = 540 "km h "^(-1)`
Speed with which the bullet will hit the thief.s car is
`v_("BT") = v_("BG")+v_("BP)+v_("PG")+v_("GT")`
`= 540 + 30 -192 " "[ :. v_("GT")=-v_("TG")]`
`= 378 " km h"^(-1) = 378 xx (1000)/(3600)" m s"^(-1) = 105 "m s"^(-1)`
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