Out of the two cars $A$ and $B$,car $A$ is moving towards the east with a velocity of $10 \, m/s$,whereas car $B$ is moving towards the north with a velocity of $20 \, m/s$. The velocity of $A$ with respect to $B$ is ......... $m/s$ (nearly).

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

Two trains,each $50 \, m$ long,are travelling in opposite directions with velocities $10 \, m/s$ and $15 \, m/s$. The time taken for them to cross each other is:

$A$ river is flowing from $W$ to $E$ with a speed of $5 \, m/min$. $A$ man can swim in still water with a velocity of $10 \, m/min$. In which direction should the man swim to take the shortest possible path to reach the opposite bank (South)?

$A$ boat crosses a river from one bank $A$ to another bank $B$ which is opposite. The distance between them is $D$. The speed of water is $V_W$ and that of the boat relative to water is $V_B$. If $V_B = 2V_W$, the time taken by the boat to cross the river directly along $AB$ is $(\sin 30^\circ = 1/2, \cos 30^\circ = \sqrt{3}/2)$.

Two persons $A$ and $B$ are located in the $X-Y$ plane at the points $(0,0)$ and $(0,10)$ respectively. (The distances are measured in $MKS$ units). At time $t=0$, they start moving simultaneously with velocities $\overrightarrow{v}_A = 2\hat{j} \text{ m/s}$ and $\overrightarrow{v}_B = 2\hat{i} \text{ m/s}$ respectively. The time after which $A$ and $B$ are at their closest distance is: