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 13.0 m/s 9.4 m/s 8.6 m/s

Explanation:

Step1: Identify the velocities as components

The boat's velocity across the river \(v_x = 8\ m/s\) (east - direction) and the river - current velocity \(v_y=5\ m/s\) (north - direction). These are perpendicular components of the resultant velocity.

Step2: Apply the Pythagorean theorem

The resultant velocity \(v\) of two perpendicular velocities \(v_x\) and \(v_y\) 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 the value and round

\(\sqrt{89}\approx9.4\ m/s\).

Answer:

9.4 m/s