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 velocities as vectors

The boat's east - ward velocity $v_x = 8$ m/s and the river's north - ward velocity $v_y=5$ m/s.

Step2: Use Pythagorean theorem for resultant velocity

The resultant velocity $v$ of two perpendicular vectors is given by $v=\sqrt{v_x^{2}+v_y^{2}}$. Substitute $v_x = 8$ and $v_y = 5$ into the formula: $v=\sqrt{8^{2}+5^{2}}=\sqrt{64 + 25}=\sqrt{89}$.

Step3: Calculate and round

$\sqrt{89}\approx9.4$ m/s.

Answer:

9.4 m/s