Question

a boat is travelling 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 9.4 m/s 13.0 m/s

Explanation:

Step1: Identify velocity vectors

Boat velocity: $v_b = 8$ m/s east, current velocity: $v_c = 5$ m/s north. These are perpendicular.

Step2: Apply Pythagorean theorem

Resultant speed $v = \sqrt{v_b^2 + v_c^2}$

Step3: Substitute values and calculate

$v = \sqrt{8^2 + 5^2} = \sqrt{64 + 25} = \sqrt{89} \approx 9.43398$

Step4: Round to nearest tenth

$v \approx 9.4$ m/s

Answer:

9.4 m/s (Option: 9.4 m/s)