a boat is traveling east across a river that is 112 meters wide at 8 meters per second. if the river has a…
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? 9.4 m/s 3.0 m/s 8.6 m/s 13.0 m/s
Answer
Explanation:
Step1: Identify the 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 the Pythagorean theorem for vector addition
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 the value
$\sqrt{89}\approx9.4$ m/s.
Answer:
9.4 m/s