Question

A steamer is heading due North with $20m{s}^{-1}$. The wind is blowing $10m{s}^{-1}$ due west. In which direction the flag on the mast flutters?

• A. ${\tan }^{-1}\frac{1}{2}$ west of north
• B. ${\tan }^{-1}\frac{1}{2}$ east of north
• C. ${\tan }^{-1}\frac{1}{2}$ north of east
• D. ${\tan }^{-1}\frac{1}{2}$ north of west

Answer 1

The correct option is A ${\tan }^{-1}\frac{1}{2}$ west of north

Flag blows in the direction which is the in the direction of relative velocity of wind with respect to steamer.

So, $v_{ws}=v_w-v_s$
Thus we, $V_{Resultant}=-20\overrightarrow{j}-10\overrightarrow{i}$ i.e. $\theta ={\tan }^{-1}\frac{-10}{20}={\tan }^1\frac{1}{2}$ west of south