A ship is travelling due east at $10\, km/hr$. $A$ ship heading $30^o$ east of north is  always due north from the first ship. The speed of the second ship in $km/hr$ is

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

Ram moves in east direction at a speed of $6 \,m / s$ and Shyam moves $30^{\circ}$ east of north at a speed of $6 \,m / s$. The magnitude of their relative velocity is ........ $m / s$

The system shown in figure is released then $a_1$ and $a_2$ is

$Assertion$ : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths.
$Reason$ : For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same.

A boat takes two hours 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