$A$ 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:

$A$ man sitting in a bus travelling from west to east with a speed of $40 \, km/h$ observes that the rain-drops are falling vertically down. To another man standing on the ground,the rain will appear:

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:

$A$ person running horizontally observes that rain is falling on his head vertically with a speed of $10\,m/s$. When he stops,he observes that the rain is falling at an angle of $30^o$ with the vertical. Find the speed with which the man was running.

Two particles $A$ and $B$ start moving from the origin in the $xy$-plane. Particle $A$ moves with a velocity of $20 \, m/s$ along the $x$-axis,and particle $B$ moves with a velocity of $30\sqrt{2} \, m/s$ at an angle of $45^{\circ}$ with the $x$-axis. The relative velocity of $B$ with respect to $A$ is ........... $m/s$.

An observer moves with a constant speed along the line joining two stationary objects. He will observe that the two objects