Question

A jet heads due west at 350 km/h. It experience a 100km/h crosswind flowing in the direction N60 degreesW.Find the speed of the jet?

Answer 1

$$\vec v=(-350, 0), \vec u=(-100\sin(60\degree), 100\cos(60\degree))$$

$$\vec v+\vec u=(-350-100\sin(60\degree), 0+100\cos(60\degree))$$

$$speed=|\vec v+\vec u|$$

$$=\sqrt{(-350-100\sin(60\degree))^2+(100\cos(60\degree))^2}$$

$$=\sqrt{350^2+70000(\dfrac{\sqrt{3}}{2})+100^2}$$

$$=100\sqrt{13.25+3.5\sqrt{3}}\ (km/h)\approx439.456\ km/h$$