Question

If a cyclist is traveling along a road due East at 10km/h and a wind is from South West at 3km/h .Find the velocity of the wind relative to the cyclist

Answer 1

$$v_r=\sqrt{(10-3\cos45°)^2+(3\sin45°)^2}=8.2\text{ km/h}.\\\space\\ \theta=\arctan\dfrac{10-3\cos45°}{3\sin45°}=74.9°\text{ W of S}.$$