Question

A political party has to start its procession in an area where wind is blowing at a speed of $30\sqrt{2}km{h}^{-1}$ and party flags on the cars are fluttering along north-east direction. If the procession starts with a speed of $40km{h}^{-1}$ towards north, find the direction of flags on the cars.

Answer 1

When the procession is stationary, the flags flutter along the north-east direction. It means wind is flowing along the north-east direction. The flags will start fluttering along the direction of the relative velocity of wind w.r.t. procession.
${\overrightarrow{v}}_{wc}={\overrightarrow{v}}_w-{\overrightarrow{v}}_c$
$=(30\sqrt{2}\cos {45}^o\hat{i}+30\sqrt{2}\sin {45}^o\hat{j})-40\hat{j}$
$=30\hat{i}-10\hat{j}\left(m{s}^{-1}\right)$
$\tan \theta =\frac{10}{30}=\frac{1}{3}$
So the flag will flutter in a direction at $\theta =ta{n}^{-1}\left(1/3\right)$ $S$ of $E$.