Adding Velocities: A Boat on a River

We start by choosing a coordinate system with its x-axis parallel to the velocity of the river. Because the boat is directed straight toward the other shore, its velocity is perpendicular to the velocity of the river. We draw the two vectors, v_boat and v_river, as shown in Figure 5.16.

Using the head-to-tail method, we draw the resulting total velocity vector from the tail of v_boat to the head of v_river.

Figure 5.16 A boat attempts to travel across a river. What is the total velocity and direction of the boat?

By using a ruler, we find that the length of the resultant vector is 7.2 cm, which means that the magnitude of the total velocity is

By using a protractor to measure the angle, we find $\theta ={32.0}^{\circ }\text{.}$