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, *v*_{p} = 30 km/h = 8.33 m/s

Muzzle speed of the bullet, *v*_{b} = 150 m/s

Speed of the thief’s car, *v*_{t}_{ }= 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:

*v*_{bt} = *v*_{b} – *v*_{t}

= 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)`