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 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

Let south to north be the positive direction of X-axis, then,
Speed of train `A,v_(A)=+54km//hr=(54xx5)/(18)m//s=15m//s`
Speed of train B, `v_(B)=-90km//hr=(-90xx5)/(18)m//s`
`=-25m//s`
(a) Relative velocity of B with respect of A is
`v_(BA)=v_(B)-v_(A)=-25-15=-40m//s`
Which means that train B appears to an observer in train A to move with a speed of 40m/s from north to south.
(b) Relative velocity of ground with respect to B is
`v_(OB)=0-0-v_(B)=0+25=25`m/s
Which means that to an observer in train B, the earth (or ground) appears to move with a speed of 25m/s from south to earth.
(c ) Let `v_(M)` be the velocity of the monkey with respect to the ground. Then, relative velocity of the monkey with respect to A is
`v_(MA)=v_(M)-v_(A)=-18` km/hr =`-5m//s`
`therefore v_(m)=v_(A)-5=(15-5)m//s`
=10m/s