Question

The heading of a plane is 27.7 degrees NE, and its air speed is 255 mi.h. If the wind is blowing from the south with a velocity of 42.0 mi/h, find the actual direction of travel of the plane, and its ground speed.
V = Vp + Vw,

V = 255mi/h @ 27.7deg + 42mi/h @ 90deg.

X=hor. = 255cos27.7 + 42cos90=225.8mi/h

Y = ver. = 255sin27.7 + 42sin90,
Y = ver = 118.53 + 42 = 160.53mi/h

tanA = Y/X = 160.53/225.8= 0.7109.
A = 35.4deg.

V = X / cosA = 225.8 / cos35.4 = 277mi/h @ 35.4deg.

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