Airplane flying in a crosswind problem

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To solve the problem of an ultralight plane flying in a crosswind, the airspeed of 45 m/s is relative to the air, not the ground. The wind is blowing at 20 m/s toward the southwest, which affects the plane's actual velocity relative to the earth. The correct approach involves calculating the x and y components of the plane's velocity by considering both the airspeed and the wind's influence. The initial attempt at finding the components yielded incorrect values, indicating a misunderstanding of the reference frame. Accurate calculations will provide the correct x and y components, along with the magnitude and angle of the plane's motion relative to the earth.
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Homework Statement



The nose of an ultralight plane is pointed south, and its airspeed indicator shows 45 m/s . The plane is in a 20 m/s wind blowing toward the southwest relative to the earth.

Find the x-component of the velocity with respect to the earth.
Find the y-component of the velocity with respect to the earth.
Find the magnitude of the plane's motion with respect to the earth.
Find the angle of the plane's motion with respect to the earth.

Homework Equations



x-component magnitude of a vector = (a)cos(\vartheta)
y-component magnitude of a vector = (a)sin(\vartheta)

The Attempt at a Solution



I mapped it all out and ended up with x and y components of -59.14 and -14.14 respectively, but this is wrong.

halp plox?
 
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halp plox?

Really?



Anyway, you realize the the airspeed indicator reading of 45 m/s is relative to the moving air, not the earth. Take that into consideration, please.
 

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