# Question about relative motion by Galilean Transformation?

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.