$A$ particle $(A)$ moves due north at $3\,km/h$ and another particle $(B)$ moves due west at $4\,km/h$. The relative velocity of $A$ with respect to $B$ is $(\tan 37^{\circ} = 3/4)$.

$A$ boy is running on a plane road with velocity $v$ with a long hollow tube in his hand. The water is falling vertically downwards with velocity $u$. At what angle to the vertical,he must incline the tube so that the water drops enter it without touching its sides?

Two particles $A$ and $B$ start moving from the origin in the $xy$-plane. Particle $A$ moves with a velocity of $20 \, m/s$ along the $x$-axis,and particle $B$ moves with a velocity of $30\sqrt{2} \, m/s$ at an angle of $45^{\circ}$ with the $x$-axis. The relative velocity of $B$ with respect to $A$ is ........... $m/s$.

$A$ 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 $\text{ m}$)

To a person,going eastward in a car with a velocity of $25\, km/hr$,a train appears to move towards north with a velocity of $25\sqrt{3}\, km/hr$. The actual velocity of the train will be..........$km/hr$

Two particles are moving along two long straight lines,in the same plane,with the same speed $= 20 \, cm/s$. The angle between the two lines is $60^{\circ}$,and their intersection point is $O$. At a certain moment,the two particles are located at distances $3 \, m$ and $4 \, m$ from $O$,and are moving towards $O$. Subsequently,the shortest distance between them will be