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? 8.6 m/s 3.0 m/s 13.0 m/s 9.4 m/s

Explanation:

Step1: Identify the velocities as perpendicular vectors

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

Step2: Apply the Pythagorean theorem for resultant velocity

The resultant velocity \( v_{resultant} \) is given by \( v_{resultant} = \sqrt{v_{boat}^2 + v_{river}^2} \). Substituting the values: \( v_{resultant} = \sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89} \approx 9.43398 \space m/s \).

Step3: Round to the nearest tenth

Rounding \( 9.43398 \) to the nearest tenth gives \( 9.4 \space m/s \).

Answer:

9.4 m/s