Question

a boat is traveling east across a river that is 112 meters wide at 8 meters per second. if the river has a northward current of 5 meters per second, what is the resultant speed of the motorboat rounded to the nearest tenth? 3.0 m/s 8.6 m/s 13.0 m/s 9.4 m/s

Explanation:

Step1: Identify the velocities as perpendicular vectors.

The boat's velocity east is \( 8 \, \text{m/s} \), and the river's current north is \( 5 \, \text{m/s} \). These are perpendicular, so we use the Pythagorean theorem.

Step2: Apply the Pythagorean theorem.

The resultant speed \( v \) is given by \( v = \sqrt{(8)^2 + (5)^2} \).
First, calculate the squares: \( 8^2 = 64 \) and \( 5^2 = 25 \).
Then, sum them: \( 64 + 25 = 89 \).
Finally, take the square root: \( v = \sqrt{89} \approx 9.4 \, \text{m/s} \).

Answer:

9.4 m/s