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

Explanation

Speed of police van , `v _(p) = 30 km h ^(-1) = ( 30 xx 1000)/( 60 xx 60) = (25)/(3) ms ^(-1)`
Speed of theft.s car, `v _(1) = 192 km h ^(-1) =( 192 xx 1000)/( 60 xx 60) = ( 160)/(3) ms ^(-1)`
Muzzle speed of bullet, `v _(b) = 150 ms ^(-1).`
The bullet is sharing the velocity of the police van, its effective velocity is
`v _(b) = v _(b) + v _(p) = 150 + ( 25)/(3) = ( 475)/(3) ms ^(-1)`
Speed of bullet w.r.t. theft.s car moving in same direction `v _(bt) = v _(b) - v _(t) =( 475)/(3) - ( 160)/( 3) = 10 5 s ^(-1).`