Two parallel rail tracks run north-south. Train A moves north with a speed of `54 km h^(-1)`, and train B moves south with a speed of `90 km h^(-1)`. What is the
(a) velocity of B with respect to A ?,
(b) velocity of ground with respect to B ?, and
(c) velocity of a monkey running on the roof of the train A against its motion (with a velocity of `18 km h^(-1)` with respect to the train A) as observed by a man standing on the ground ?

Explanation

`v_A=+54 "km h"^(-1)=15 ms^(-1)`
`v_B=-90 "km h"^(-1) = -25 ms^(-1)`
Relative velocity of B with respect to A is
`V_(BA)=V_B-V_A=-40 ms^(-1)`
i.e. the train B appears to A to move with a speed of `40 m s^(-1)` from north to south.
Relative velocity of ground with respect to B is
`V_(GB)=0-v_B=25m s^(-1)`
In (c), let the velocity of the monkey with respect to ground be `v_M`. Relative velocity of the monkey with respect to A.
`v_(MA)=v_M-v_A=-18 "km h"^(-1)=-5 m s^(-1)`
Therefore , `v_M=v_(MA)+v_A =(-5+15)m s^(-1)=10 ms^(-1)`