Two parallel rail tracks run north south. Trains A moves north with a speed of 54km h^(-1), and train B moves south with a speed of 90km h^(-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 velocity of 18kmh^(-1) with respect to the train A) as observed by a man standing on the ground?

Two parallel rail tracks run north south. Trains A moves north with a

1.	Two parallel rail tracks run north south. Trains A moves north with a speed of 54km h^(-1), and train B moves south with a speed of 90km h^(-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 velocity of 18kmh^(-1) with respect to the train A) as observed by a man standing on the ground?
Answer» Solution :`v_(A)=+54km h^(-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)`.