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.
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: $\displaystyle 6^2 + 3^2 = h^2 $
So, $\displaystyle 36 + 9 = h^2 $
$\displaystyle h^2 = 45 $
We are only concerned with the positive root. Thus, h = $\displaystyle \sqrt{45} $
So, your speed and direction is $\displaystyle 3\sqrt{5} $ km/h NE .
-Andy