Two parallel rail tracks run north-south. Train A moves north with a speed of 54 k mh−1 and train B moves south with a speed of 90 kmh−1. The relative velocity of B w.r.t. A is

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Two parallel rail tracks run north-south. Train A moves north with a speed of $54 k m h^{- 1}$ and train B moves south with a speed of $90 k m h^{- 1} .$ The relative velocity of B w.r.t. A is

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$- 40 m s^{- 1}$

$- 20 m s^{- 1}$

$50 m s^{- 1}$

$- 30 m s^{- 1}$

answer is A.

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Detailed Solution

Let positive direction of motion be from south to north.
Given, $v_{A} = + 54 k m h^{- 1} = 15 m s^{- 1};$

$v_{B} = - 90 k m h^{- 1} = 25 m s^{- 1}$

$∴$ The relative velocity of B w.r.t. A

$v_{B A} = v_{B} - v_{A} = - 25 - 15 = - 40 m s^{- 1}$

i. e. , the train B appears to A to move with a speed of $40 m s^{- 1}$ from north to south.

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