physics
posted by Anonymous .
The pilot of an aircraft wishes to fly due west in a 46.8 km/h wind blowing toward the south. The speed of the aircraft in the absence of a wind is 204 km/h.
(a) In what direction should the aircraft head?
° north of west
(b) What should its speed relative to the ground be?
km/h

a. X = 204 km/h.
Y = 46.8 km/h.
tanA = Y/X = 46.8/204 = 0.22941.
Ar = 12.9o South of West.
The plane should head 12.9o North of West.
b. A = 180 + Ar = 180 + 12.9 = 192.9o
V = X/cosA = 204/cos192 = 209.3 km/h. 
a. Vpa = Vpg + Va = 204 km/h
Vpg  46.8i = 204
Vpg = 204 + 46.8i
Tan Ar = Y/X = 46.8/204 = 0.22941
Ar = 12.9o = Reference angle.
A = 12.9 + 180 = 167.1o CCW = 12.9o N.
of W. = Direction.
b. Vpg = X/Cos A = 204/Cos167.1 = 209.3 m/s. = Velocity of plane relative to gnd.