Q. A police jeep is chasing with velocity of $45\, km/h$ a thief in another jeep moving with velocity $153\,km/h$. Police fires a bullet with muzzle velocity of $180\, m/s$. The velocity it will strike the car of the thief is:

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A

150 m/s

B

27 m/s

C

450 m/s

D

250 m/s

Solution:

Bullet will strike the car, when striking speed is equal to relative speed of bullet with respect to car.
Since, police jeep and thief are moving in the same direction relative velocity is
$\ce{->[{\text { Police jeep }}][{v_{1}=45 km / h }]} \ce{->[{\text { Thief }}][{v_{2}=153 km / h }]}$
$\vec{V}_{r}=\vec{V}_{1}-\vec{V_{2}} $
$=153-45=108 \,km / h$
$=108 \times \frac{5}{18}=30\, m / s$
Bullet will hit the thief's car when relative speed of bullet with respect to thief's car $180-30=150$ $m / s$ is equal to striking speed of bullet.

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