Kinematics Vectors and cartesian coordinates. Plane with wind blowing.

[freddyb]

Homework Statement

An airplane flies at an air speed of 300 miles per hour, in the direction toward southwest. There is a head wind of 75 mi/hr in the direction toward due east.
(A) Determine the ground speed.

(B) Determine the direction of motion of the plane, expressed as an angle counterclockwise from due east.

Homework Equations

Va=airspeed
w=wind speed
V=velocity relative to ground

V=(w-Va/sqrt2)i+(-Va/sqrt2)j

*i & j are constants

direction θ = 180 + arctan|Vy/Vx|

The Attempt at a Solution

Totally stumped any help would be greatly appreciated!

 

[e^(i Pi)+1=0]

Decompose vector 1 into x & y components, add vector 2, recompose into final vector.