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? 9.4 m/s 13.0 m/s 8.6 m/s 3.0 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 can use the Pythagorean theorem.

Step2: Apply the Pythagorean theorem

The resultant speed \( v \) is given by \( v = \sqrt{v_{east}^2 + v_{north}^2} \), where \( v_{east} = 8 \) and \( v_{north} = 5 \).
So \( v = \sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89} \approx 9.4 \, \text{m/s} \).

Answer:

9.4 m/s