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
9.4 m/s
3.0 m/s
13.0 m/s

Explanation:

Step1: Identify perpendicular velocities

The boat's eastward speed $v_x = 8$ m/s, river's northward speed $v_y = 5$ m/s.

Step2: Apply Pythagorean theorem

Resultant speed $v = \sqrt{v_x^2 + v_y^2}$
$$v = \sqrt{8^2 + 5^2}$$

Step3: Calculate the value

$$v = \sqrt{64 + 25} = \sqrt{89} \approx 9.43398$$

Step4: Round to nearest tenth

Round $9.43398$ to one decimal place.

Answer:

9.4 m/s