Kinematics Vectors and cartesian coordinates. Plane with wind blowing.

AI Thread Summary
An airplane flying southwest at 300 miles per hour encounters a headwind of 75 miles per hour from the east. To find the ground speed, the vectors must be decomposed into their x (east-west) and y (north-south) components. The resultant vector is calculated by adding these components, followed by recomposing to determine the final velocity. The direction of motion is expressed as an angle counterclockwise from due east, calculated using the arctangent function. This problem illustrates the application of kinematics, vectors, and Cartesian coordinates in real-world scenarios.
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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!
 
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Decompose vector 1 into x & y components, add vector 2, recompose into final vector.
 

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