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

3

Explanation

`V_(A)=+54 km h^(-1)=15 ms^(-1)`
`V_(B)=-90 km h^(-1)=-25 ms^(-1)`
Relative velocity of B with respect to A is
`V_(BA)=V_(B)-V_(A)=-40 ms^(-1)`
i.e. the train B appears to A to 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)=25 ms^(-1)`
In ( C) let the velocity of the monkey with respect to ground to `V_(M)`.Relative velocity of the monekey with respect to A.
`V_(MA)=V_(M)-V_(A)=-18 kmh^(-1)=-5 ms^(-1)`
Therefore , `V_(M)=V_(MA)+V_(A)=(-5+15) ms^(-1)=10 ms^(-1)`.