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 positive direction of motion be from south to north. Then ,
`v_(A) = + 534 km h^(-1) =15 ms^(-1)` :
`v_(B) =- 90 km h^(-1) =- 25 ms^(-1)`
(a) Relative velocity of `B w , r, t, A`
`=v_(AB) =v_(B) -v_(A) =- 25 -15 =- 40 ms^(-1)`
i.e. teain (B) appears to (A) move with a speed of `40 ms^(-1)` from borth to south.
(b) Relative velocity of ground w.r.t. (B)
`=0-v_(B) =0 -(-25) =25 ms^(-1)` dur north
(c ) Let `v_(m) be the velocity of monkey w.r.t. train (A) ` =v_(m) -v_(A) =- 18 km h^(-1) =- 5 ms^(-1)`
:. `v_(m) =v_(A) -5 =15 =10 ms^(-1)` due north `.