Assumed that north is the y-direction and east the x-direction.
You are piloting the boat that moves at a constant speed of 10 km/hr relative to the water beneath it.
1) On a body of still water, you point your boat due north for 2hr, then turn due east and continue for another 3 hr. What is your displacement vector and average velocity vector over this trip?
2) Suppose now that the water flows southward with a constant speed of 5km/hr while you attempt the same trip in part 1: point your boat due north for 2hr, then turn due east for 3 hr. What would be your displacement vector and the average velocity vector relative to earth over this trip?
1) Pythagorean and tan-1 for magnitude and direction. Ave vel is total displacement (which you found from pythagorean) over total time.
2) add in a southward displacement of 5km/hr times 5hr = 25 km south. Essentially you are cancelling the 20 km and making it 5 km south.