Answer:
Step-by-step explanation:
Given
Initially Plane is flying at the speed of [tex]180\ km/hr[/tex]
to the [tex]15^{\circ}[/tex] North of east
Now wind started Blowing and plane started moving towards east with speed [tex]150\ km/hr[/tex]
suppose [tex]1v_o[/tex] is the speed of wind
So,
[tex]\vec{v_2}=\vec{v_1}-\vec{v_o}[/tex]
[tex]150\hat{i}=180[\cos 15\hat{i}+\sin 15\hat{j}]-\vec{v_o}[/tex]
[tex]\vec{v_o}=\hat{i}[180\cos 15-150]+\hat{j}[180\sin 15][/tex]
[tex]\vec{v_o}=\hat{i}[173.866-150]+46.58\hat{j}[/tex]
[tex]\vec{v_o}=23.86\hat{i}+46.58\hat{j}[/tex]
So magnitude of wind is
[tex]\mid v_o\mid=\sqrt{23.86^2+46.58^2}[/tex]
[tex]\mid v_o\mid=\sqrt{2738.996}[/tex]
[tex]\mid v_o\mid=52.33\ km/hr[/tex]
direction [tex]\tan \theta=\frac{46.58}{23.86}[/tex]
[tex]\theta =62.87^{\circ}[/tex] North of east
