Two cars $A$ and $B$ are moving with the same speed of $45\,km/h$ along the same direction. If a third car $C$ coming from the opposite direction with a speed of $36\,km/h$ meets the two cars in an interval of $5\,min$,the distance of separation between the two cars $A$ and $B$ should be.......$km$.

Two towns $A$ and $B$ are connected by a regular bus service with a bus leaving in either direction every $T$ minutes. $A$ man cycling with a speed of $20 \; km/h$ in the direction $A$ to $B$ notices that a bus goes past him every $18 \; min$ in the direction of his motion,and every $6 \; min$ in the opposite direction. What is the period $T$ (in $min$) of the bus service and with what speed (assumed constant) do the buses ply on the road?

$A$ swimmer can swim in still water with $5 \,m/s$. If a river is flowing with $4 \,m/s$, then find the time to cross the river of width $300 \,m$ if he has to reach the exactly opposite point.

$A$ boat takes $2 \, h$ to travel $8 \, km$ and back in still water. If the velocity of water is $4 \, km/h$,the time taken for going upstream $8 \, km$ and coming back is:

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

$A$ boy runs on a horizontal road with a speed of $4 \ m \ s^{-1}$ while it is raining. He sees that the rain is making an angle $\theta$ with the vertical while running from west to east. However, when he runs from east to west, the angle is $\alpha$. The rain is pouring down at an angle $45^{\circ}$ with the vertical and at a speed of $8 \ m \ s^{-1}$ as shown in the figure. The ratio $\frac{\tan \theta}{\tan \alpha}$ is,