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) 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 18 km h^(-1) with respect to the train A) as observed by a man standing on the ground ?

Two parallel rail tracks run north-south. Train A moves north with a s

1.	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) 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 18 km h^(-1) with respect to the train A) as observed by a man standing on the ground ?
Answer» Solution :Choose the positive direction of x-axis to be from SOUTH to north. Then, `upsilon_(A)=+54 km h^(-1) = 15 ms^(-1)` `upsilon_(B)=-90 km h^(-1)=-25 ms^(-1)` Relative velocity of B with respect to `A=upsilon_(B)-upsilon_(A)=-40 ms^(-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=0-upsilon_(B)=25 ms^(-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^(-1)=-5 ms^(-1)`. Therefore, `upsilon_(M)=(15-5)ms^(-1)=10 ms^(-1)`.