$A$ swimmer crosses a river of width $d$ flowing at velocity $v$. While swimming,he heads himself always at an angle of $120^{\circ}$ with the river flow and on reaching the other end he finds a drift of $d/2$ in the direction of flow of river. The speed of the swimmer with respect to the river 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?

Preeti reached the metro station and found that the escalator was not working. She walked up the stationary escalator in time $t_1$. On other days,if she remains stationary on the moving escalator,then the escalator takes her up in time $t_2$. The time taken by her to walk up on the moving escalator will be

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:

$A$ thief's car is moving with a speed of $10\,m/s$. $A$ police van chasing this car with a speed of $5\,m/s$ fires a bullet at the thief's car with a muzzle velocity of $72\,km/h$. Find the speed with which the bullet will hit the car in $m/s$.

$A$ boat crosses a river with a velocity of $8 \, km/h$ relative to the water. If the resultant velocity of the boat with respect to the ground is $10 \, km/h$,then the velocity of the river water is...........$km/h$.