A police van moving on a highway with a speed of 30 km `h^(-1)` fires a bullett at a thief's car speeding away in the same direction with a speed of 192 km `h^(-1)`. If the muzzle speed of the bullet is 150 `ms^(-1)`, with what speed does the bullet hit the thief's car ? (Note : Obtain that speed which is relevant for damaging the thief's car).

Explanation

Muzzle speed of bullet, `upsilon_(B)=150 m//s=540" km "h^(-1)`
Speed of police van , `upsilon_(P)=30km//h`
Speed of theif car, `upsilon_(T)=192km//h`
Since the bullet is sharing the velocity of the police van, its effective velocity is
`" "v_(B)=upsilon_(B)+upsilon_(P)=540+30=570km//h`
The speed of bullet w.r.to the theifs car moving in the same direction.
`v_(BT)=v_(B)-upsilon_(T)=570-192=378 km//h`
`" "=(378 times 1000)/(60 times 60)=105m//s`