SOLUTION: The instruments of an airplane show a speed of 165 mph on a heading of 210degrees. However, the computer shows a ground speed of 178 mph on a heading of 212degrees. Find the speed

Algebra ->  Length-and-distance -> SOLUTION: The instruments of an airplane show a speed of 165 mph on a heading of 210degrees. However, the computer shows a ground speed of 178 mph on a heading of 212degrees. Find the speed       Log On


   

Question 316091: The instruments of an airplane show a speed of 165 mph on a heading of 210degrees. However, the computer shows a ground speed of 178 mph on a heading of 212degrees. Find the speed and direction of the wind.
Thanks you so much for helping me.
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
resolving the airspeed and ground speed into their x and y components will allow you to find the wind speed components

remember to convert the compass heading to degrees on the unit circle

Ax = 165 * cos(240º) = -82.5

Ay = 165 * sin(240º) = -142.89 (approx)

Gx = 178 * cos(238º) = -94.33 (approx)

Gy = 178 * sin(238º) = -150.95 (approx)

Wx = Gx - Ax = -11.83

Wy = Gy - Ay = -8.06

W = sqrt(Wx^2 + Wy^2) = 14.31 (approx)

Θ = tan^-1(Wy / Wx) = 214.27º (approx)

the heading of the wind is 235.73º (approx)