Suppose that a wind is blowing in the direction S45°E at a speed of 50 km/h. A pilot is steering a plane in the direction N60°E at an airspeed (speed in still air) of 150 km/h. The true course, or track, of the plane is the direction of the resultant of the velocity vectors of the plane and the wind. The ground speed of the plane is the magnitude of the resultant. Find the true course and the ground speed of the plane. (Round your answers to one decimal place.)

Question

I got that the vectors for the wind and the pane were <50cos(45),-50sin(45)> and <150cos(60),150sin(60)> respectively. So then I added them together in order to find the true course and ground speed. But it seems this is not correct at N40.6E and 145.3km/h.

Answer 1

Vr=50[315oCCW] + 150[30oCCW] = Resultant
velocity.

X = 50*Cos315 + 150*Cos30 = 165.3 km.
Y = 50*sin3i5 + 150*sin30 = 39.64 km.

Tan A = Y/X = 39.64/165.3 = 0.23981.
A = 13.5o.

Vr=X/Cos A=165.3/Cos13.5 = 170km[13.5o]
CCW. = 170km[N76.5oE].