Question

Two parallel rail tracks run north-south. On one track train A moves north with a speed of $ 54 \,km \,h^{-1} $ and on the other track train $ B $ moves south with a speed of $ 90\, km\, h^{-1} $ . The velocity of train $ A $ with respect to train $ B $ is

• A. $ 10\, ms^{-1} $
• B. $ 15\, ms^{-1} $
• C. $ 25\, ms^{-1} $
• D. $ 40\, ms^{-1} $

Answer 1

Answer: (D)

Let the positive direction of motion be from south to north.
Velocity of train $ A $ with respect to ground

$ v_{AG}=+54\,km\,h^{-1}=+54\times\frac{5}{18}\,ms^{-1}=+15\,ms^{-1} $
Velocity of train $ B $ with respect to ground
$ v_{BG}=-90\,km\,h^{-1}=-90\times\frac{5}{18}\,ms^{-1}=-25\,ms^{-1} $
Relative velocity of train $ A $ with respect to train $ B $ is
$ v_{AB}=v_{AG}+v_{GB}=v_{AG}-v_{BG}\quad\left(Q\,v_{GB}=-v_{BG}\right) $
$ =+15\,ms^{-1}-\left(-25\,ms^{-1}\right)=40\,ms^{-1} $