Question

A police van moving on the highway with a speed of 30 km/h fires a bullet at the thief's car speeding away in the same direction with speed of 192 km/h. If the nuzzle speed of the bullet is 150 m/s, with what speed does the bullet hit the thief's car? ​

Answer 1

Speed of the Police van = 30km/h = 8.33m/s

Nuzzle Speed of the Bullet = 150 m/s

Speed of the Thief's car = 192km/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 :

= 158.33 - 53.33 = 105 m/s

Hence , The bullet hits the Thief's car at 105m/s speed.

Answer 2

velocity of police Vp = 30km/hr = 25/3 m/s

velocity of thief Vt = 190km/hr = 160/3 m/s

velocity of bullet which police fires Vb = 150 m/s

final velocity of the bullet muzzle from gun = Vb + Vp = 150 + 25/30 = 475/3 m/s

let velocity of thief be zero seen with respect to thief .

Velocity of thief w.r.t thief

Vb/t = Vb - Vt = 475/3 - 160/3 = 105 m/s