$A$ boat is sent across a river with a velocity of $8 \, km/hr$. If the resultant velocity of the boat is $10 \, km/hr$,then the velocity of the river is ........ $km/hr$.

The speed of a swimmer is $4\,km\,h^{-1}$ in still water. If the swimmer makes his strokes normal to the flow of a river of width $1\,km$,he reaches a point $750\,m$ downstream on the opposite bank. The speed of the river water is $.........\,km\,h^{-1}$.

$A$ man standing on a road holds his umbrella at $30^\circ$ with the vertical to keep the rain away. He throws the umbrella and starts running at $10 \, km/h$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the moving man will be:

$A$ girl standing on a road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she starts running without an umbrella with a speed of $15 \sqrt{2} \; kmh^{-1}$,the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is ........... $kmh^{-1}$

$A$ man can swim with velocity $v$ relative to water. He has to cross a river of width $d$ flowing with a velocity $u$ $(u > v)$. The distance through which he is carried downstream by the river is $x$. Which of the following statements is correct?

$A$ shell is fired at a speed of $200\ m/s$ at an angle of $37^o$ above the horizontal from the top of a tower $80\ m$ high. At the same instant,another shell is fired from a jeep travelling away from the tower at a speed of $10\ m/s$ as shown. The velocity of this shell relative to the jeep is $250\ m/s$ at an angle of $53^o$ with the horizontal. Find the time (in $sec$) taken by the two shells to come closest.