Resultant vectors

**kkaa** · February 26th 2010, 08:25 AM

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?

**mathaddict** · February 26th 2010, 08:23 PM

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 ,

$|V_w|^2=425^2+414^2-2(425)(414)\cos 20$

$|V_w|=146.09 km/h$

As for the direction , solve for $\alpha$ first

sine rule ,

$\frac{146.09}{\sin 20}=\frac{414}{\sin \alpha}$

$\alpha=75.75^o$

$\theta=90-75.75=14.25$

so the direction is S 14.25 E

**kkaa** · February 26th 2010, 08:49 PM

how did you know the direction of wind supposes tobe

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