1)If I head across a river paddling my canoe at 6km/h N, but the river current is moving at 3km/h E, determine the speed and direction of my canoe relative to the shore.
This is simply a vector addition problem. The resultant vector will be the hypotenuse of the right triangle you construct as well as its direction.
The math bit:
We are only concerned with the positive root. Thus, h =
So, your speed and direction is km/h NE .