An aircraft maintains a constant speed of 500 mph with the b

An aircraft maintains a constant speed of 500 mph with the bearing 140 degrees.The velocity of the wind is 80 mph in the bearing of 42 degrees. Find the actual speed and direction.

Solution

V = 500mph[140deg] +8[42 deg]

X = 500*cos140+ 8cos42 = -377.07 mph
Y = 500*sin140 + 8sin42 =326.75 mph.

tanA = -377.07/ 326.75 =-1.154
A = 180-49 = 131 deg

V = X/cosA = 377.07/cos131 = 574.76mph (Actual speed)