Question

A girl at summer camp is rowing her one-person canoe across a river at a 45° angle to the bank upstream with a force of 4540N. (See diagram.) If the current is pushing her boat downstream at 6079 N, what is the net force on the boat?

Answer 1

$$\vec{F}_{net}=(4540\sin{45},6079-4540\cos{45})=\\(3210,2869)\ N$$

Magnitude is

$$F_{net}=\sqrt{3210^2+2869^2}=4305\ N$$

Direction

$$\theta=\arctan{\frac{3210}{2869}}=48.2\degree\text{ to the bank downstream}$$