# Thread: Resultant vectors

1. ## Resultant vectors

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?

2. Originally Posted by kkaa
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

3. how did you know the direction of wind supposes tobe