$A$ car with a vertical windshield moves in a rainstorm at a speed of $40 \, km/h$. The raindrops fall vertically with a constant speed of $20 \, m/s$. The angle at which the raindrops strike the windshield is .........

$A$ ship $X$ moving due north with speed $v$ observes that another ship $Y$ is moving due west with the same speed $v$. The actual velocity of $Y$ is $........$.

$A$ man standing on a road has to hold 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 actual speed of raindrops is:

Airplanes $A$ and $B$ are flying with constant velocity in the same vertical plane at angles $30^{\circ}$ and $60^{\circ}$ with respect to the horizontal,respectively,as shown in the figure. The speed of $A$ is $100 \sqrt{3} \ m/s$. At time $t=0$,an observer in $A$ finds $B$ at a distance of $500 \ m$. This observer sees $B$ moving with a constant velocity perpendicular to the line of motion of $A$. If at $t = t_0$,$A$ just escapes being hit by $B$,then $t_0$ in seconds is:

The speed of a swimmer in still water is $20 \; m/s$. The speed of river water is $10 \; m/s$ and is flowing due east. If he is standing on the south bank and wishes to cross the river along the shortest path,the angle at which he should make his strokes with respect to north is given by ......$^o$ west.

$A$ 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.