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Question: Two parallel rail tracks run north-south. On one track train A moves north with a speed of 54 km h<s...

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

10ms−110ms^{- 1}

B

15ms−115ms^{- 1}

C

25ms−125ms^{- 1}

D

40ms−140ms^{- 1}

Answer

40ms−140ms^{- 1}

Explanation

Solution

Let the positive directions of motions be from south to north.

Velocity of train A with respect to ground

VAG=+54kmh−1=+54×518ms−1=+15ms−1V_{AG} = + 54kmh^{- 1} = + 54 \times \frac{5}{18}ms^{- 1} = + 15ms^{- 1}

Velocity of train B with respect to ground

vBG=−90kmh−1=−90×518ms−1=−25ms−1v_{BG} = - 90kmh^{- 1} = - 90 \times \frac{5}{18}ms^{- 1} = - 25ms^{- 1}

Relative velocity of train A with respect to train B is

VAB=VAG+VGB=VAG−VBGV_{AB} = V_{AG} + V_{GB} = V_{AG} - V_{BG} (∵VGB=−VBG\because V_{GB} = - V_{BG})

=+15ms−1−(−25ms−1)=40ms−1+ 15ms^{- 1} - ( - 25ms^{- 1}) = 40ms^{- 1}