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 `kmh^(-1)`. What is the
a) velocity of B with respect to A ?
b) velocity of ground with respect to B ?
c) velocity of a monkey running on the roof of the train A against. Its motion (with a velocity of 18 `kmh^(-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)=15ms^(-1)`
`upsilon_(B)=-90" km "h^(-1)=-25ms^(-1)`
Relative velocity of B with respect to `A=upsilon_(A)-upsilon_(B)=-40ms^(-1)`, i.e., the train B appears to A to move with a speed of 40 `ms^(-1)` from north to south.
Relative velocity of ground with respect to B `=0-upsilon_(B)=25ms^(-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^(-)=-5mh^(-1)`.
Therefore, `upsilon_(M)=(15-5)mh^(-1)=10mh^(-1)`.