$A$ glass windscreen,whose inclination with the vertical can be changed,is mounted on a car. The car moves horizontally with a speed of $2\,m/s$. At what angle $\alpha$ with the vertical should the windscreen be placed so that the rain drops falling vertically downwards with velocity $6\,m/s$ strike the windscreen perpendicularly?

$A$ boat moves with a speed of $5 \, km/h$ relative to water in a river flowing with a speed of $3 \, km/h$ and having a width of $1 \, km$. The minimum time taken for a round trip is ......... $min$.

$A$ man walking briskly in rain with speed $v$ must slant his umbrella forward making an angle $\theta$ with the vertical. $A$ student derives the following relation between $\theta$ and $v: \tan \theta = v$ and checks that the relation has a correct limit: as $v \rightarrow 0, \theta \rightarrow 0,$ as expected. (We are assuming there is no strong wind and that the rain falls vertically for a stationary man). Do you think this relation can be correct? If not,guess the correct relation.

Rain is falling at an angle of $30^{\circ}$ from the vertical due to the wind with a speed of $40 \ m/s$. $A$ car is travelling horizontally in the direction opposite to the wind,at a speed of $40 \ m/s$. At what angle from the vertical will it experience the rain falling from (in $^{\circ}$)?

The figure shows two ships moving in the $x-y$ plane with velocities $V_A$ and $V_B$. The ships move such that $B$ always remains north of $A$. The ratio $\frac{V_A}{V_B}$ is equal to ........

$A$ flag is mounted on a car moving due North with a velocity of $20 \, km/hr$. Strong winds are blowing due East with a velocity of $20 \, km/hr$. The flag will point in which direction?