Question

when a boat travels with a velocity of 8 km/h across a river, and the combined effect of the rivers flow makes its resultant speed 10 km/h, determine the rivers velocity.
a 6 km/h
b 4 km/h
c 8 km/h
d 2 km/h

Explanation:

Step1: Apply Pythagorean theorem

Let the boat's velocity across the river be $v_b = 8\ km/h$ and the resultant velocity be $v_r=10\ km/h$. Let the river's velocity be $v_{river}$. Since the boat's velocity across the river and the river - flow velocity are perpendicular (in a typical river - crossing scenario), we have $v_r^{2}=v_b^{2}+v_{river}^{2}$.

Step2: Solve for river's velocity

$v_{river}=\sqrt{v_r^{2}-v_b^{2}}=\sqrt{10^{2}-8^{2}}=\sqrt{100 - 64}=\sqrt{36}=6\ km/h$

Answer:

A. $6\ kmh^{-1}$