Question

A bird is flying due east with a velocity of $4m{s}^{-1}$. The wind starts to blow with a velocity of $3m{s}^{-1}$ due north. What is the magnitude of relative velocity of bird w.r.t. wind? Find out.its direction also.

Answer 1

The velocity of bird with respect to wind can be given as
${\overrightarrow{v}}_{b.w}={\overrightarrow{v}}_b-{\overrightarrow{v}}_w$
$={\overrightarrow{v}}_b+(-{\overrightarrow{v}}_w)$
$=4\hat{i}+(-3\hat{j})\left(m{s}^{-1}\right)$
$=4\hat{i}-3\hat{j}\left(m{s}^{-1}\right)$
$|{\overrightarrow{v}}_{b.w}|=\sqrt{(4{)}^2+(3{)}^2}$
$=5m{s}^{-1}$
Here the direction of the relative velocity of the bird is
$|tan\beta |=\frac{3}{4}\Rightarrow \beta =ta{n}^{-1}\left(\frac{3}{4}\right)$
Hence, the relative velocity of the bird with respect to wind is $5m{s}^{-1}$ and in the direction $ta{n}^{-1}\left(\frac{3}{4}\right)$ from east toward south.