Answer to Question #240833 in Physics for razvan

Question

A boat attempts to travel straight across to the other side of a river. The boat can go 21 m/s and the river travels at 12 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's denote $v = 21m/s$ the speed of the boat with respect to water, $v_w$ the speed of the water with respect to shore, $v'$ is the speed of the boat with respect to shore (according to the task it should be perpendicular to the shore), $\theta$ is the angle the boat needs aim upstream to dock exactly on the other side of the river.

From the right triangle below obtain:

$$\theta = \arcsin\left( \dfrac{12m/s}{21m/s} \right) \approx 35\degree$$

Answer. 35 degrees.