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

Choose the positive direction of x-axis to be from south to north. Then,
`upsilon_(A)=+54 km h^(-1) = 15 ms^(-1)`
`upsilon_(B)=-90 km h^(-1)=-25 ms^(-1)`
Relative velocity of B with respect to `A=upsilon_(B)-upsilon_(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=0-upsilon_(B)=25 ms^(-1)`.
In (c), let the velocity of the monkey with respect to ground be `upsilon_(M)`. Relative velocity of the monkey with respect to A,
`upsilon_(MA)=upsilon_(M)-upsilon_(A)=-18 km h^(-1)=-5 ms^(-1)`. Therefore, `upsilon_(M)=(15-5)ms^(-1)=10 ms^(-1)`.