Finding Velocity and Direction in a Crosswind: Aircraft Navigation Problem

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To navigate westward in a 50 km/h south wind, the aircraft must adjust its heading to counteract the wind's effect. The required calculations involve determining the angle and speed that balance the wind's influence while maintaining a westward trajectory. The correct heading angle should be approximately 14.48 degrees north of west, with a resultant ground speed of about 193.6 km/h. The pilot is struggling with the trigonometric calculations necessary to find these values. Accurate application of vector components is essential for successful navigation in crosswinds.
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Ok, here's the problem.. What am I doing wrong??

The pilot of an aircraft wishes to fly due west in a wind blwoing at 50 km/h toward the south. If the speed of the aircraft in the absence of wind is 200 km/h, in what durection should the aircraft head and what should its speed be relative to the ground?

I keep getting Velocity of 216 and 14.05 direction and its not right??!? HELP! :mad:
 
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To fly west, the plane must have a west component, and there must be a northern velocity component to offset the southbound wind.

Take the planes velocity magnitdue to be 200, which must be at some angle west of north (to offset the wind).

So 200*f(a) = 50, where f is some trig function and a is the angle.
 
I still can't get the right answer...
 
By any chance, is the answer 14.48 degree and 193.6km/h?
 
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