$A$ person is swimming with a speed of $10\, m/s$ at an angle of $120^{\circ}$ with the flow of the river and reaches a point directly opposite on the other side. If the speed of the river flow is $x\, m/s$,find the value of $x$ to the nearest integer.

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:

$A$ 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 cars are moving in the same direction with the same speed $30 \, km/hr$. They are separated by a distance of $5 \, km$. The speed of a car moving in the opposite direction,if it meets these two cars at an interval of $4 \, minutes$,will be.......$km/hr$.

$A$ ship $X$ moving due north with speed $v$ observes that another ship $Y$ is moving due west with the same speed $v$. The actual velocity of $Y$ is $........$.

$A$ car travels with a speed of $40 \text{ km h}^{-1}$. Rain drops are falling at a constant speed vertically. The traces of the rain on the side windows of the car make an angle of $30^{\circ}$ with the vertical. The magnitude of the velocity of the rain with respect to the car is