SOLUTION: To a motor-cyclist traveling due north at 50km/hr, the wind appear to come from north west at 60km/hr, what is the true velocity of the wind

1.  Let's consider more simple case first:


        Let there is no wind at the coordinate system which rests relative the Earth,
        and a motor-cyclist travels due North at 50 km/h.


    Then it is clear that he/she will observe the wind due to south at 50 km/h.

    I other words, he/she will observe the wind with the vector  (0,-50)  (the units of speed are in km/h).



2.  Then it is clear, that if there is the wind with the velocity vector  W 
    
    in the coordinate system which rests relative the Earth surface, and 

    the motor-cyclist moves at the speed  M  (! M is vector !), then the wind he/she will observe is  = W - M.



3.  With these explanations, we have 


        - the vector  M = (0,50) of the motor-cyclist speed relative the Earth;

        - the vector   = (,)

         - and the equation   = (,) = W - (0,50).


    From this equation, the "real" vector of the wind velocity in the resting coordinate system is


        W = (,) + (0,50) = (,).


    Now, when you know the vector W by its components, you can easily calculate its magnitude.


    It is just arithmetic, and I leave it to you to complete this assignment on your own.