Question

A man can swim in still water at a speed of 6kmph and he has to cross the river and reach just opposite point on the other bank. if the river is flowing at a speed of 3kmph, he has to swim in the direction

Answer 1

Final Answer : $tan^{-1}(1/2)$ with the vertical.

Steps :
1) Man has to swim in such a way that, he want to reach just opposite point on the other bank.
=> Drift is 0 .

2)Speed of River is 3km/h in horizontal direction.
=> For Drift to be zero, Horizontal component of velocity of man should be 3km/h leftward.
as shown. We get,
$|v_x| = 3 km/h \\ |v_y| = 6 km/h \\ => \tan(\theta) = \frac{|v_x|}{|v_y|} \\ => \tan(\theta) = \frac{1}{2}$

Hence, Man has to swim by making angle $\theta$ with vertical.