Answer to Question #138930 in Physics for hannah

Question

The airspeed of a small plane is 215 km/h. The wind is blowing at 57 km/h from the west. Determine the velocity of the plane in m/s relative to the ground if the pilot keeps the plane aimed in the direction [34° E of N].

Answer 1

$$V^2=v^2+v_w^2-2vv_w\cos{(90+34)}\\V^2=215^2+57^2-2(215)(57)\cos{124}\\V=251\frac{km}{h}$$

$$\sin{\theta}=\frac{57\sin{124}}{251}\to \theta=11\degree\\$$

The direction is

$$34+11=45\degree \text{ E of N}$$