You are piloting a small airplane in which you want to reach a destination that

Question

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 a strong but steady wind) to maintain a northerly course you must point the nose of the plane at an angle of 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 4.32 h. A fellow pilot calls to ask you about the wind velocity (magnitude and direction). What is your report?

A detail response of the Galiliean Transformation Would be very helpful. Trying to understand how to do sucha problem.

Explanation / Answer

so yor normal speed is 750/3.14

you have to angle your plane so that there is no x component

so in x direction

-750/3.14*sin(22) +x = 0

so x component of wind = 750/3.14*sin(22 degrees)=89.48 km/hr

in y direction

750/3.14*cos(22) + y = 750/4.32

y=-47.85 km/hr

so magnitude = sqrt(89.48^2 + 47.85^2)=101.47 km/hr

direction = arctan(y/x) = arctan(-47.85/89.48)= -28.14 degrees

so 28.14 degrees south of east

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