Two paarallel 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. relaity of a monkey running on the roof of the train `A` against its motion (with its velocity of `18 km h^(1)` with respect ot the train `A` ) as observed by a man standing on the fround?

Explanation

a. `vec v_(BA)=vec v_(B)-vec v_(A)`
Taking south direction as positive. `v_(BA)=90-(-54)=144 km h^(-1)`
Hence, velocity of train `A` w,r,t train `A` is `44 km h^(-1)` toward south.
b. Vilocity of train w.r.t `B` train `B` is `90 km h^(-1)` towards north.
c. `v_("monkey,hround")=`?
`vec v_(m,g)= vec v_(m,A)+vec v_(Ag)=18-54=-36 km h^(-1)`
Hence, velocity of monkey will be `36 km h^(-1)` toward north.`