Question

north at 16 m/s across a river that flows at 9.0 m/s. what is the speed of the boat? options: 26 m/s, 0 m/s, 16 m/s, 18 m/s

Explanation:

Step1: Identify the velocities

The boat's velocity relative to the water is \( v_{boat} = 16 \, \text{m/s} \) north, and the river's velocity is \( v_{river} = 9.0 \, \text{m/s} \) (assuming the river flows east or west, perpendicular to north). These are perpendicular vectors.

Step2: Use the Pythagorean theorem

The resultant speed \( v \) of the boat (relative to the ground) is given by the magnitude of the vector sum of the boat's velocity and the river's velocity. Since they are perpendicular, we use \( v = \sqrt{v_{boat}^2 + v_{river}^2} \).

Substitute \( v_{boat} = 16 \, \text{m/s} \) and \( v_{river} = 9.0 \, \text{m/s} \):

\[
v = \sqrt{16^2 + 9^2} = \sqrt{256 + 81} = \sqrt{337} \approx 18 \, \text{m/s}
\]

Answer:

18 m/s (corresponding to the option with 18 m/s)