Question

A boat can move with a speed of $5\text{km/h}$ in still water. A river is flowing with a speed of $3\text{km/h}$ and having a width of $10\text{km}$. The minimum time taken for a round trip to the exact same point is

• A. $1\text{hr}$
• B. $2\text{hr}$
• C. $3\text{hr}$
• D. $4\text{hr}$

Answer 1

The correct option is D $4\text{hr}$

Given:
$V_{Br}=5\text{km/h};V_r=3\text{km/h}$

For the minimum time of round trip, he should cross perpendicular to the river.

While going:


Velocity of boat with respect to river $\left(V_{Br}\right)$ in the direction perpendicular to the river is given by

$V_{Br}=\sqrt{(V_B^2-V_r^2)}=\sqrt{5^2-3^2}$

$\Rightarrow V_{Br}=4\text{m/s}$

$\therefore$ Time for trip to that side will be

$t=\frac{8\text{km}}{4\text{km/hr}}=2\text{hr}$

To come back, again he takes $2\text{hr}$ to cross the river.

$\therefore$ Minimum time taken around a round trip is $4\text{hr}$.

Hence, option $\left(d\right)$ is correct.

$$\begin{array}{c}\text{Why this question?}\\ \text{For crossing the river with the shortest}\\ \text{path, the velocity of boat w.r.t ground}\\ \text{must be perpendicular to river.}\end{array}$$