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

Options

A. `10 m s^(-1)`
B. `15 m s^(-1)`
C. `25 m s^(-1)`
D. `40 m s^(-1)`

Answer

D

Explanation

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 xx 5/18 m s^(-1) = +15 m s^(-1)`
Velocity of train B with respect of ground
`v_(BG) = -90- km h^(-1) = -90 xx 5/18 m s^(-1) = -25 m s^(-1)`
Relative velocity of train A with respect to train B is
`v_(AB) = v_(AG) + v_(GB) = v_(AG) - v_(BG) (Q v_(GB) = -v_(BG))`
`+15 m s^(-1) - (-25 m s^(-1) = 40 m s^(-1))`