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?
Answer
Explanation:
Step1: Identify vector - like components
The boat's speed across the river is $v_x = 8$ m/s (east - direction) and the river's current speed is $v_y=5$ m/s (north - direction). These are perpendicular to each other.
Step2: Apply Pythagorean theorem for resultant speed
The resultant speed $v$ of the boat 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