Question

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 ?

• A. $ 95 \,m \,s^{-1} $
• B. $ 105 \,m \,s^{-1} $
• C. $ 115 \,m \,s^{-1} $
• D. $ 125 \,m \,s^{-1} $

Answer 1

Answer: (B)

Speed of police van w.r.t. ground
$ \therefore v_{PG}=30\,km\,h^{-1} $
Speed of thief’s car w.r.t. ground
$ \therefore v_{TG}=192\,km\,h^{-1} $
Speed of bullet w.r.t. police van
$ v_{BP}=150\,ms^{-1}=150\times\frac{18}{5}km\,h^{-1}=540\,km\,h^{-1} $
Speed with which the bullet will hit the thief’s car will be
$ v_{BT}=v_{BG}+v_{GT}=v_{BP}+v_{PG}+v_{GT} $
$ =540\,km\,h^{-1}+30\,km\,h^{-1}-192\,km\,h^{-1} $
$ \left(\because v_{GT}=-v_{TG}\right) $
$ =378\,km\,h^{-1}=378\times\frac{5}{18}\,ms^{-1}=105\,ms^{-1} $