What is the speed of the current in the direction of the canoe's motion?

Question

A canoe is moving with velocity v=<5,3> m/s relative to the water. The velocity of the current in the water is c=<1,2> m/s. Solution is 1.89 m/s.

Answer 1

Use vector projection of the current vector onto the vector representing the position of the canoe:

$$\frac{5+6}{25+9}*<5,3> = \frac{11}{34}<5,3> = <\frac{55}{34}, \frac{33}{34}>$$

Magnitude: $\sqrt{\left(\frac{55}{34}\right)^2 + \left(\frac{33}{34}\right)^2} = 1.89 \text{m/s}$

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