A girl standing on road holds her umbrella at $45^{\circ}$ with the vertical to keep the rain away. If she starts running without 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 boat takes two hours to travel $8 \,km$ and back in still water. If the velocity of water is $4\, km/h$, the time taken for going upstream $8 \,km$ and coming back is

Rain is falling vertically with a speed of $35 \;m s ^{-1} .$ A woman rides a bicycle with a speed of $12 \;m s ^{-1}$ in east to west direction. What is the direction in which she should hold her umbrella?

A ship is travelling due east at $10\, km/hr$. $A$ ship heading $30^o$ east of north is  always due north from the first ship. The speed of the second ship in $km/hr$ is

Ram moves in east direction at a speed of $6 \,m / s$ and Shyam moves $30^{\circ}$ east of north at a speed of $6 \,m / s$. The magnitude of their relative velocity is ........ $m / s$

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.......$km/hr$