Two parallel rail tracks run north-south. Train A moves north with a speed of `54kmh^(-1)`, and train B moves south with a speed of `90kmh^(-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 velocityof `18 kmh^(-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)`.