Question

A man can swim in still water at a speed of 6 km/h 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 3 km/h, he has to swim in the direction

• A. $\tan \left(\theta \right)=\frac{1}{2}$
• B. $\tan \left(\theta \right)=\frac{3}{2}$
• C. $\tan \left(\theta \right)=\frac{\sqrt{3}}{2}$
• D. $\tan \left(\theta \right)=\frac{5}{2}$

Answer 1

The correct option is A $\tan \left(\theta \right)=\frac{1}{2}$

1) A man has to swim in such a way that, he want to reach just the opposite point on the other bank.

=> Drift is 0 .

2)The speed of the River is 3km/h in the horizontal direction.

=> For Drift to be zero, a Horizontal component of velocity of man should be

3km/h leftward.

We get,

$|v_x|=3km/h|v_y|=6km/h$

$=>\tan \left(\theta \right)=\frac{|v_x|}{|v_y|}$

$=>\tan \left(\theta \right)=\frac{1}{2}$