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:

So,

We are only concerned with the positive root. Thus, h =

So, your speed and direction is km/h NE .

-Andy