Answer to Question #96927 in Physics for Dude

Question

So here’s the question.

If plane is flying 350 km/h, North 35 degrees West and the winds is blowing at 60 kilometres per hour, South 26 degrees West, then find the plane’s resultant velocity. (might need diagrams since it’s vector question)

Answer 1

$$\bold{v_p}=(350\cos{35},350\sin{35})\frac{km}{h}$$

$$\bold{v_w}=(60\cos{26},-60\sin{26})\frac{km}{h}$$

$$\bold{V}=(350\cos{35},350\sin{35})+(60\cos{26},-60\sin{26})$$

$$\bold{V}=(340.6,174.4)\frac{km}{h}$$

The plane’s resultant velocity:

$$V=\sqrt{340.6^2+174.4^2}=383\frac{km}{h}$$

$$\theta=\arctan{\frac{174.4}{340.6}}=N\ 27.1\degree \ W$$