$A$ boat is moving with a velocity $3i + 4j$ with respect to the ground. The water in the river is moving with a velocity $-3i - 4j$ with respect to the ground. The relative velocity of the boat with respect to the water is:

$A$ man swimming downstream overtakes a float at a point $M$. After travelling a distance $D$,he turns back and passes the float at a distance of $D/2$ from the point $M$. The ratio of the speed of the swimmer with respect to still water $(v_s)$ to the speed of the river $(v_r)$ is:

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

$A$ man can swim with a speed of $4 \ km/h$ in still water. How long does he take to cross a river $1 \ km$ wide, if the river flows steadily at $3 \ km/h$ and he makes his strokes normal to the river current (in $min$)?

$A$ 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 $\text{ m}$)

On a calm day,a boat can go across a lake and return in time $T_0$ at a speed $V$. On a rough day,there is a uniform current at speed $v$ that helps the onward journey and impedes the return journey. If the time taken to go across and return on the rough day is $T$,then $T / T_0$ is: