A police van moving on a highway with a speed of `30 kmh^(-1)` fires a bullet at a thief's car speeding away in the same direction with a speed of `192 kmh^(-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

Velocity of thief.s car `v _(t) =192 km//hr = (192 xx 1000)/(3600) ms ^(-1) `
`v _(t) = (160)/(3) ms ^(-1)`
Velocity of police.s car `v _(p) = 30 km //h`
`= (30 xx 1000)/(3600) ms ^(-1) = (25)/(3) ms ^(-1)`
Muzzle velocity of bullet,
`v _(b). = 150 ms ^(-1)`
`therefore` velocity of bullet `v _(b) = v _(p) + v _(b) = (25)/(3) + 150 `
`v _(b) = (475)/(3) ms ^(-1)`
Velocity of bullet while striking thief.s car = velocity of bullet w.r.t. their `v_(bt)`
But `v _(bt) =v_(b) -v_(t)`
`= (475)/(3) - (160)/(3) = (315)/(3) `
`v _(bt) = 105 ms ^(-1)`
Second method:
`v _(t) =192 km //h = (160)/(3) ms ^(-1)`
`v _(p) = 30 km//h = (25)/(3) ms ^(-1)`
Velocity of theif.s car w.r.t. olice.s car `v _(tp) =v_(t) - v _(p)`
`=(160)/(3) - (25)/(3)`
`v _(rp) = 45 ms ^(-1)`
Muzzle velocity of bullet
`v _(b). = 150 ms ^(-1)`
= velocity of bullet w.r.t. police.s car = `v_(bp)`
Velocity of bullet while striking thief.s car,
`= v _(bp) - v _(tp)`
`= 150 -45`
`= 105 ms ^(-1)`