Rain is falling vertically with a speed of $30 \,m/s$. A man rides a bicycle with a speed of $10 \,m/s$ from East to West direction. At what angle with the vertical does he see the rain falling?

When is the relative velocity of two moving cars greater than the individual velocity of both cars?

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

$A$ steamboat goes across a lake and comes back $(a)$ on a quiet day when the water is still and $(b)$ on a rough day when there is a uniform air current so as to help the journey onward and to impede the journey back. If the speed of the launch on both days was the same,in which case will it complete the journey in lesser time?

$A$ river has a steady speed of $v$. $A$ man swims upstream for a distance of $d$ and swims back to the starting point in a total time $t$. The man can swim at a speed of $2v$ in still water. If the time taken by the man in still water is $t_0$ to complete the same total distance of $2d$, then $\frac{t}{t_0}$ is

$A$ swimmer swims in still water at a speed of $5 \text{ km/hr}$. He enters a $200 \text{ m}$ wide river,having a river flow speed of $4 \text{ km/hr}$,at point $A$ and proceeds to swim at an angle of $127^{\circ}$ $(\sin 37^{\circ} = 0.6)$ with the river flow direction. Another point $B$ is located directly across $A$ on the other side. The swimmer lands on the other bank at a point $C$,from which he walks the distance $CB$ with a speed of $3 \text{ km/hr}$. The total time in which he reaches from $A$ to $B$ is .......... $\text{minutes}$.