A police van moving on a highway with a speed of 30 km h–1 fires a bullet 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 m s–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).
Solution 1
Speed of the police van, vp = 30 km/h = 8.33 m/s
Muzzle speed of the bullet, vb = 150 m/s
Speed of the thief’s car, vt = 192 km/h = 53.33 m/s
Since the bullet is fired from a moving van, its resultant speed can be obtained as:
= 150 + 8.33 = 158.33 m/s
Since both the vehicles are moving in the same direction, the velocity with which the bullet hits the thief’s car can be obtained as:
vbt = vb – vt
= 158.33 – 53.33 = 105 m/s
Solution 2
Speed of police van = `v_p = 30 kmh^(-1) = 30xx1000/3600 ms^(-1) = 25/3 ms^(-1)`
Speed of thiefs car = v_t = 192 `"km h"^(-1)`
`=192 xx 5/18 ms^(-1) = 160/3 ms^(-1)`
Speed of bulletv_b = Speed of police van + speed with which bullet is actually fired
`:. v_b =(25/3 + 150)ms^(-1) = 475/3 ms^(-1)`
Relative velocity of bullet w.r.t theif's car
`v_(bt) = v_b - v_t = (475/3 - 160/3) ms^(-1) = 105 ms^(-1)`
