A plane is to fly due north. The speed of the plane relative to the air is 200 km/h, and the wind is blowing from west to east at 90 km/h

a) Since the wind is blowing toward the east, the plane must head west of north as shownin figure. The velocity of the plane relative to the ground ${\overrightarrow{v}}_{pg}$ will be the sum of the velocity of the plane relative to the air ${\overrightarrow{v}}_{pa}$ and the velocity of the air relative to the ground ${\overrightarrow{v}}_{ag}$

b) 1. The velocity of the plane relative to the ground is given by equation:

  ${\overrightarrow{v}}_{pg}={\overrightarrow{v}}_{pa}+{\overrightarrow{v}}_{ag}$

 2. The sine of the angle $\theta$ between the velocity of the plane and north equals the ration of   $v_{ag}$ and  $v_{pa}$

$\sin \theta =\frac{v_{ag}}{v_{pa}}=\frac{90km/m}{200km/h}=0.45$

c) Since $v_{ag}$ and $v_{pg}$ are perpendicular, we can use the Pythagorean theorem to find the magnitude of ${\overrightarrow{v}}_{pg}$.

$v_{pa}^2=v_{ag}^2+v_{pg}^2$            

$v_{pg}=\sqrt{v_{pa}^2-v_{ag}^2}$    

$=\sqrt{{\left(200km/h\right)}^2-{\left(90km/h\right)}^2}=179km/h$