A river is flowing from $W$ to $E$ with a speed of  $5 \,m/min$. A man can swim in still water with a velocity $10\, m/min$. In which direction should the man swim so as to take the shortest possible path to go to the south.

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

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 man can swim with velocity $v$ relative to water. He has to cross a river of width $d $ flowing with a velocity $u (u > v)$. The distance through which he is carried down stream by the river is $x$. Which of the following statement is correct

$Assertion$ : The magnitude of velocity of two boats relative to river is same. Both boats start simultaneously from same point on one bank may reach opposite bank simultaneously moving along different paths.
$Reason$ : For boats to cross the river in same time. The component of their velocity relative to river in direction normal to flow should be same.

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