Question

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

• A. 105 m/s
• B. 205 m/s
• C. 210 m/s
• D. 250 m/s

Answer 1

Answer: (A)

Speed of thiefs car w.r.t. ground
$ {{v}_{T}}=192\,km/h $
Speed of police van w.r.t. ground
$ {{v}_{P}}=30\,km/h $
Speed of bullet w.r.t. police van
$ {{v}_{B}}=150\,m/s=540\,km/h $
Speed with which the bullet will hit the thiefs car will be
$ v={{v}_{BG}}+{{v}_{GT}} $
$ v={{v}_{B}}+{{v}_{P}}+{{v}_{T}} $
$ =540+30-192 $
$ [\because \,{{v}_{G}}=-{{v}_{T}}] $
$ =378\,km/h $ $ =378\times \frac{1000}{3600}\,m/s $
$ =105\,m/s $