Question

A boat is travelling east at 500km/h in relaxed water. When a stable 100 km/h wave hits from north to south, at what direction and angle will the sailor have to maintain the same course?

Answer 1

The sailor will need to go in NE direction to maintain the same course, but at different speed. The angle can be found from the figure:

The final velocity is the resultant vector, the angle is

$$\theta=\text{arccos}\frac{100}{500}=78.48°\text{ E of N}$$