Question

A jet airliner, moving initially at 260 mi/h to the east, suddenly enters a region where the wind is blowing at 100 mi/h toward the direction 30.0° north of east. What is the new speed and direction of the aircraft relative to the ground?

Answer 1

Break up each vector into components:\[\overrightarrow{V}=\overrightarrow{V_P}+\overrightarrow{V_A}=<260,0>+<100\cos(30^{\circ}),100\sin(30^{\circ})>\]Add the vectors together, the magnitude of the resulting vector will be your total speed\[|\overrightarrow{V}|=\sqrt{({\text{x-component})^2+(\text{y-component})^2}}\]