calculate velocity and direction

Question

An aeroplane can travel @ 15km/h in still air. The wind blowing @ 50km/h due south west. Calculate: 1. The direction in which the pilot must steer in order to travel due north. 2. The velocity of the aeroplane in relation to the ground.

Answer 1

The westward velocity due to wind is 50 km/h * sin(45) = 35.36 km/h.

So the eastward component of the plane's 150 km/h must be 35.36 km/h.

Hence the angle θ between the pilot's direction and a due north direction is given by:

150 sin(θ) = 35.36.

θ = 13.63^o.

The pilot must steer 13.63^o east of due north.

Find the ground speed  of air plane.

V_ground = (150 km/h)*cos(13.63^o) + (50 km/h)*cos(45^o) = 145.76 + 35.36 = 181 km/h.