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. relative velocity of `B` with respect to `A`?
b. relative velocity of a monkey running on the roof of the train `A` against its motion (with its velocity of `18 km h^(1)` with respect to the train `A` ) as observed by a man standing on the ground?

Explanation

`v_(A)=+54kmh^(-1)=15ms^(-1)`
`v_(B)=-90kmh^(-1)=-25ms^(-1)`
Relative velocity of B with respect to A is
`V_(BA)=V_(B)-V_(A)=-40ms^(-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)=25ms^(-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)=-18kmh^(-1)=-5ms^(-1)`
Therefore, `v_(M)=v_(MA)+v_(A)=(-5+15)ms^(-1)=10ms^(-1)`.