Question

A bird is flying towards east with v=4m/s with respect
to ground. The wind is blowing with v=3 m/s towards
north then find magnitude of Respective Velocity of a bird
with respect to wind find its direction.​

Answer 1

Given

A bird is flying towards east with v = 4 m/s with respect  to ground. The wind is blowing with v = 3 m/s towards  north

To Find

Magnitude of relative velocity of a bird with respect to wind .

Solution

Let the velocity of bird be $\rm \vec{v}_b$

Velocity of wind be $\rm \vec{v}_w$

So , the velocity of the bird with respect to wind is given by ,

$\rm \vec{v}_{bw}\\\\\to\ \rm \vec{v}_b-\vec{v}_w\\\\\to\ \rm \vec{v}_b+(-\vec{v}_w)\\\\\to\ \rm 4 \hat{i}+(3\hat{j})$

$\rm So, \vec{v}_{bw}=4\hat{i}+3\hat{j}$

Now , we need to find the magnitude of relative velocity of a bird with respect to wind .

$\to\ \rm |\vec{v}_{bw}|=\sqrt{4^2+3^2}\\\\\to\ \rm |\vec{v}_{bw}|=\sqrt{16+9}\\\\\to\ \rm |\vec{v}_{bw}|=\sqrt{25}\\\\\to\ \rm |\vec{v}_{bw}|=5\ m/s$

Direction is given by ,

$\to \rm tan\ \alpha =\dfrac{a}{b}\\\\\to \rm tan\ \alpha=\dfrac{3}{4}\\\\\to \rm \alpha=tan^{-1}\bigg( \dfrac{3}{4}\bigg)$

and direction is from east towards south .