Question

A boat travels west at a speed of 24m/s across a river that is flowing south at 9m/s. What is the resultant velocity of the boat?

Answer 1

The resultant velocity is the sum of the two vectors: the velocity of boat and the velocity of river. Since they are perpendicular to each other, the magnitude of their sum can be found using the Pythagorean theorem:

$$v_{res} = \sqrt{24^2+9^2} \approx 25.63m/s$$

The direction is:

$$\theta = \arctan\left(\dfrac{9}{24} \right) \approx 20.56\degree$$

Answer. 25.63 m/s, 20.56 degree South of the West.