An airplane is travelling S70W with a resultant ground speed of 414 km/h. The nose of the plane is pointing west with an airspeed of 425 km/h. Determine is the speed and direction of the wind.
how to solve it?
hi
you will need a diagram to solve this , take a look at the one i attached .
using the cosine rule ,
$\displaystyle |V_w|^2=425^2+414^2-2(425)(414)\cos 20$
$\displaystyle |V_w|=146.09 km/h$
As for the direction , solve for $\displaystyle \alpha$ first
sine rule ,
$\displaystyle \frac{146.09}{\sin 20}=\frac{414}{\sin \alpha}$
$\displaystyle \alpha=75.75^o$
$\displaystyle \theta=90-75.75=14.25$
so the direction is S 14.25 E