Question

A boat attempts to travel straight across to the other side of a river. The boat can go 18 m/s and the river travels at 17 m/s. At what angle (to the nearest degree) does the boat need aim upstream to dock exactly on the other side of the river?

Answer 1

Let $\mathbf{v}_w$ be the vector of river velocity with magnitude $v_w = 17m/s$ and $\mathbf{v}$ be the vector of boat velocity with magnitude $v = 18 m/s$. Than, adding these two vectors together as shown in the second figure above, obtain the vector $\mathbf{v}'$ that should point North:

$$\mathbf{v}' = \mathbf{v}_w + \mathbf{v}$$

From the right triangle obtain angle $\theta$ the boat needs aim upstream to dock exactly on the other side of the river:

$$\sin\theta =\dfrac{v_w}{v} = \dfrac{17}{18}\\ \theta \approx 71\degree$$

Answer. $71\degree$.