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You are piloting a small airplane in which you want to reach a destination that is 750 km due north of your starting location. Once you are airborne, you find that (due to strong but steady wind) to maintain a northerly course you must point the nose of the plane at an angle that is 22◦ west of true north. From previous flights on this route in the absence of wind, you know that it takes you 3.14 h to make the journey. With the wind blowing, you find that it takes 4.32h. A fellow pilot calls you to ask about the wind velocity (magnitude and direction). What is your report?

My approach: I am trying to solve this by Galilean Transformation. I consider one ground frame and another frame is an airplane. So we need to calculate the Velocity of the wind w.r.t plane. That I am thinking. I have doubt about choosing my frame of reference.

$V_{W/G}$ = $V_{W/P}$ + $V_{P/G}$.

$V_{P/G}$ = -(750/4.32)*sin(22)i + (750/4.32)cos(22)j

I am not able to calculate. The answer is 101km/h and 62 degrees east of south. Am I am choosing my frame of references right or not? I will appreciate any help.

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