$A$ 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 $10 \ km/hr$. He finds that raindrops are hitting his head vertically. The speed of raindrops with respect to the road will be ......... $km/hr$.

$A$ 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 ........... $kmh^{-1}$

$A$ 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:

$A$ man is running on a level road with a speed of $10 \ m/s$. He feels that the rain is falling vertically downward with a speed of $10 \sqrt{3} \ m/s$. If he runs in the opposite direction with the same speed,then the speed of the rain relative to him will be:

$A$ swimmer can swim with a velocity of $12 \, km/h$ in still water. The water flowing in a river has a velocity of $6 \, km/h$. The angle with respect to the direction of flow of the river water at which the swimmer should swim in order to reach the point on the other bank just opposite to his starting point is ........$^{\circ}$. (Round off to the Nearest Integer)

$A$ 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