Kinematics Vectors and cartesian coordinates. Plane with wind blowing.

freddyb

1. The problem statement, all variables and given/known data

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.


2. Relevant 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|



3. 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.