A boat is moving with velocity of $3\hat i + 4\hat j$ in river and water is moving with a velocity of $ - 3\hat i - 4\hat j$ with respect to ground. Relative velocity of boat with respect to water is :

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 uniform current at speed $v$ to help the onward journey and impede the return journey. If the time taken to go across and return on the rough day be $T$, then $T / T_0$ is

A swimmer can swim with speed '$v$' with respect to still water in a river which is flowing with speed $u$. There is a float moving with the river. Now the swimmer overtakes float and gets a lead of $l$ and returns back to the float. Time taken by swimmer in this process will be

Out of the two cars $A$ and $B$, car $A$ is moving towards east with a velocity of $10 \,m / s$ whereas $B$ is moving towards north with a velocity $20 \,m / s$, then velocity of A w.r.t. $B$ is ......... $m / s$ (nearly)

The speed of a swimmer in still water is $20 \;\mathrm{m} / \mathrm{s}$. The speed of river water is $10\; \mathrm{m} / \mathrm{s}$ 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 w.r.t. north is given by ......$^o$ west

A boat crosses a river with a velocity of $8\, km/h$. If the resulting velocity of boat is $10 \,km/h $ then the velocity of river water is...........$km/h$