An airplane pilot sets a compass course due west and maintains an airspeed of 225km/h . After flying for a time of 0.520h , she finds herself over a town a distance 122km west and a distance 15km south of her starting point.

Question

Part A
Find the magnitude of the wind velocity.
v = km/h
Part B
Find the direction of the wind velocity.
Express your answer as an angle measured south of west
θ =∘ south of west
Part C
If the wind velocity is 42km/h due south, in what direction should the pilot set her course to travel due west? Use the same airspeed of 225km/h .
Express your answer as an angle measured north of west
θ = ∘ north of west

Answer 1

X = -122 km
Y = -15 km

Vw = d/t = 15/0.52 = 28.8 km/h

B. Tan Ar = Y/X = -15/-122 = 0.12295
Ar = 7.0o = Reference angle.
A = 7 + 180 = 187o = 7o S of W.

C. X = 225 km/h.
Y = 42 km/h.

Tan A = 42/225 = 0.18667
A = 10.57o S of W.
Pilot should head 10.57o N of W.