Question

A river has a current flowing with a velocity of 2.0 meters per second due east. A boat travels at 3.0 meters per second relative to the river and is headed due north. In the adjacent diagram, the vector starting at point P represents the velocity of the boat relative to the river water. What is the direction of the resultant velocity relative to the south riverbank? 12 degrees34 degrees56 degrees78 degrees

Answer 1

First let's draw the vectors that correspond to the boat speed and the river speed.

The river speed is 2 m/s due east, and the boat speed is 3 m/s due north, so we have:

Addind these vectors, the resultant is:

In order to calculate the angle x, we can use the tangent relation, which is the opposite side to the angle over the adjacent side to the angle:

$\begin{gathered} \tan (x)=\frac{3}{2} \\ \tan (x)=1.5 \\ x=56.31\degree \end{gathered}$

So the direction of the resultant is 56 degrees.