The maximum speed of a boat in still water is $27 \,km/h$. Now this boat is moving downstream in a river flowing at $9 \,km/h$. $A$ man in the boat throws a ball vertically upwards with a speed of $10 \,m/s$. The range of the ball as observed by an observer at rest on the river bank is . . . . . . $cm$. (Take $g = 10 \,m/s^2$)

$A$ bird is tossing (flying to and fro) between two cars moving towards each other on a straight road. One car has a speed of $54 \text{ kmh}^{-1}$ while the other has a speed of $36 \text{ kmh}^{-1}$. The bird starts moving from the first car towards the other and is moving with a speed of $36 \text{ kmh}^{-1}$ when the two cars are separated by $36 \text{ km}$. The total distance covered by the bird before the cars meet each other is: (in $\text{ m}$)

$A$ bird is flying to and fro between two cars moving towards each other on a straight road. One car has a speed of $18\,km/h$ while the other has a speed of $27\,km/h$. The bird starts moving from the first car towards the other with a speed of $36\,km/h$. If the two cars were initially separated by $36\,km$,what is the total distance covered by the bird?

$A$ slider block $A$ moves downward at a speed of $v_A = 2 \ m/s$,at an angle of $75^\circ$ with the horizontal as shown in the figure. The velocity of the portion of belt $B$ between ideal pulleys $C$ and $D$ with respect to $A$ is $v_{CD/A} = 2 \ m/s$ at an angle $\theta$ with the horizontal. The magnitude of the velocity of portion $CD$ of the belt when $\theta = 15^\circ$ is .......... $m/s$.

$A$ particle $(A)$ moves due north at $3\,km/h$ and another particle $(B)$ moves due west at $4\,km/h$. The relative velocity of $A$ with respect to $B$ is $(\tan 37^{\circ} = 3/4)$.

$A$ 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: