$A$ bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of $54 \text{ kmh}^{-1}$ while the other has a speed of $36 \text{ kmh}^{-1}$. The bird starts moving from the first car towards the other and is moving with a speed of $36 \text{ kmh}^{-1}$ when the two cars are separated by $36 \text{ km}$. The total distance covered by the bird before the cars meet each other is: (in $\text{ m}$)

$A$ river is flowing with a velocity of $5 \ km/hr$ as shown in the figure. $A$ boat starts from $A$ and reaches the other bank. The width of the river is $b = 300 \ m$. The velocity of the boat in still water is $v_{br} = 3 \ km/hr$. If the boat aims to reach the point directly opposite to $A$ (point $B$),but due to the river flow,it reaches point $C$,what is the distance $AC$ covered by the boat? (Note: The boat is steered such that it maintains a straight path relative to the ground).

$A$ man is running at a speed of $5 \, m/s$. The rain drops appear to be falling at an angle of $45^{\circ}$ from the vertical. If the rain drops are actually falling vertically downwards,then the velocity of the rain drops (in $m/s$) is:

If a $100 \,m$ long train needs $7.2 \,s$ to cross an object moving in a direction opposite to the train's direction with a speed of $5 \,km/h$, then find the velocity of the train. (in $\,km/h$)

$A$ passenger sitting in a train $A$ moving at $90\,km/h$ observes another train $B$ moving in the opposite direction for $8\,s$. If the velocity of the train $B$ is $54\,km/h$,then the length of train $B$ is $..........\,m$.

$A$ steamboat goes across a lake and comes back $(a)$ on a quiet day when the water is still and $(b)$ on a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both days was the same,in which case will it complete the journey in lesser time?