$A$ 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.

$A$ police van moving on a highway with a speed of $30\; km/h$ fires a bullet at a thief's car speeding away in the same direction with a speed of $192\; km/h.$ If the muzzle speed of the bullet is $150\; m/s,$ with what speed (in $m/s$) does the bullet hit the thief's car?

$A$ 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 $..........\,m$.

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:

$A$ train is moving slowly on a straight track with a constant speed of $2 \,ms^{-1}$. $A$ passenger in that train starts walking at a steady speed of $2 \,ms^{-1}$ to the back of the train in the opposite direction of the motion of the train. To an observer standing on the platform directly in front of that passenger, the velocity of the passenger appears to be:

Two trains, each $30 \,m$ long, are travelling in opposite directions with velocities $5 \,m/s$ and $10 \,m/s$. They will cross each other after: (in $\,s$)