Math: Calculus - Algebraic Vectors

[K_Swiss]

A light plane is travelling at 175 km/h on a bearing of N8°E in a 40 km/h wind from N80°E. Determine the plane's ground velocity using algebraic vectors.


I drew the diagram for this problem:

[attachment=0:1xxbwdoc]Algebraic Vectors 3.png[/attachment:1xxbwdoc]

Green = Resultant
Blue = 40 km/h wind from N80°E
Red = 175 km/h on a heading of N8°E
? = missing resultant and angle

This is how far I got and now I don't know what to do.

I don't know how to find the angle to put into the following equation:

(a , b) = ( | r | * cos? , | r | * sin? )

Please help me by doing a step by step solution to this problem!


The answer for this question is:

167 km/h , N5°W

 

[tkhunny]

Why isn't it just a subtraction problem?

Rather than 175cis(82º)+40cis(10º), for the resultant Air Speed and Heading, your buddies on the ground are fooled by the effects of the wind. Find, 175cis(82º)-40cis(10º).

You have the orange guy in your drawing. Find it.