When a train is at rest,rain drops fall vertically. When it moves along east with a velocity equal to that of rain,the rain will appear to fall,for a passenger in the train

Consider two observers observing a single moving object,and one observer observing two moving objects. Explain the concept of relative velocity in these scenarios.

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 velocity of $B$ with respect to $A$?

$A$ swimmer can swim with a velocity of $12 \, km/h$ in still water. The water flowing in a river has a velocity of $6 \, km/h$. The angle with respect to the direction of flow of the river water at which the swimmer should swim in order to reach the point on the other bank just opposite to his starting point is ........$^{\circ}$. (Round off to the Nearest Integer)

$A$ river has a steady speed of $v$. $A$ man swims upstream for a distance of $d$ and swims back to the starting point in a total time $t$. The man can swim at a speed of $2v$ in still water. If the time taken by the man in still water is $t_0$ to complete the same total distance of $2d$, then $\frac{t}{t_0}$ is

$A$ passenger train of length $60\, m$ travels at a speed of $80\, km/hr$. Another freight train of length $120\, m$ travels at a speed of $30\, km/hr$. The ratio of times taken by the passenger train to completely cross the freight train when:
$(i)$ they are moving in the same direction,and
$(ii)$ in the opposite directions is