$A$ 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:

$A$ river is flowing from west to east at a speed of $8\,m/min$. $A$ man on the south bank of the river,capable of swimming at $20\,m/min$ in still water,wants to swim across the river in the shortest time. He should swim in a direction

$A$ swimmer can swim in still water with speed $v$ and the river is flowing with velocity $v/2$. To cross the river in the shortest distance,the swimmer should swim at an angle $\theta$ with the upstream. What is the ratio of the time taken to swim across in the shortest time to the time taken to swim across the shortest distance?

$A$ boy is running on a plane road with velocity $v$ with a long hollow tube in his hand. The water is falling vertically downwards with velocity $u$. At what angle to the vertical,he must incline the tube so that the water drops enter it without touching its sides?

Two parallel rail tracks run north-south. Train $A$ moves north with a speed of $54\; km\; h^{-1},$ and train $B$ moves south with a speed of $90\; km\; h^{-1}.$ What is the velocity (in $m\; s^{-1}$) of a monkey running on the roof of the train $A$ against its motion (with a velocity of $18\; km\; h^{-1}$ with respect to the train $A$) as observed by a man standing on the ground?

$A$ man is crossing a river flowing with a velocity of $5\, m/s$. He reaches a point directly across at a distance of $60\, m$ in $5\, s$. His velocity in still water should be ........ $m/s$.