Question

A river flows due east at 2.20 m/s. A boat crosses the river from the south shore to the north shore at a speed of 13.0 m/s due north relative to the water. What is the velocity of the boat as viewed by an observer on the shore?

A. 13.0 m/s
B. 11.5 m/s
C. 2.20 m/s
D. 14.5 m/s

Answer 1

The velocity of the boat as viewed by an observer on the shore is 13.16 m/s, 9.54° north of the east direction.

Step-by-step explanation:

To find the velocity of the boat as viewed by an observer on the shore, we need to consider the boat's velocity relative to the water and the velocity of the river.

Since the boat is crossing the river due north at a speed of 13.0 m/s and the river is flowing due east at 2.20 m/s, we can find the resultant velocity using vector addition.

The magnitude of the resultant velocity is given by the Pythagorean theorem as √((13.0 m/s)^2 + (2.20 m/s)^2) = 13.16 m/s. The direction of the resultant velocity can be found using the inverse tangent function as tan^(-1)(2.20 m/s/13.0 m/s) = 9.54° north of the east direction.