A boat is moving in a river with a velocity of $5\text{ m/s}$ relative to the water. The river is $100\text{ m}$ wide and flows at $3\text{ m/s}$. The minimum time taken to cross the river is:

Solution

1. The time to cross is $t=\frac{d}{v_y}$, where $d$ is the width and $v_y$ is the velocity component perpendicular to the bank.
2. To minimize $t$, we must maximize $v_y$.
3. The maximum value of $v_y$ is the full magnitude of the boat's velocity relative to the water, which is $5\text{ m/s}$.
4. Thus, $$\begin{array}{rl}{t}_{min}& =\frac{100}{5}\\ & =20\text{ s}\end{array}$$.
5. Hence the answer is (A).