Solve Airplane & Wind Homework: 640m/s at 57o E of S?

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A plane with a maximum airspeed of 770 m/s needs to achieve a ground velocity of 640 m/s at 57° E of S while facing a wind velocity of 150 m/s at 48° W of S. The initial calculation yielded a velocity of 686.6 m/s at 19° S of E, but the final solution was adjusted to 694.11 m/s at 20.9° S of E. The discussion highlights the importance of vector addition in solving the problem. The pilot can achieve the desired ground velocity with the calculated heading and speed.
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Homework Statement


A plane has a max airspeed of 770m/s. If the wind velocity is 150m/s 48o W of S, in what direction and with what velocity should the pilot fly the plane to have a ground velocity of 640m/s at 57o E of S? Can She do it?



Homework Equations


V(plane to wind) + V(wind to ground) = V(airplane to ground)


The Attempt at a Solution


Well, I actually got to some answer, but I need someone to help me check if it is correct. If not, can you please help me?

For velocity and direction I got 686.6m/s at 19o S of E.

Thank you!
 
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nvm i solved it on my own.. i got 694.11m/s 20.9 S of E
 

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