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).

A police van moving on a highway with a speed of 30 kmh^(-1) fires a b

1.	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).
Answer» <P> Solution :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)`