Question

A man can row a boat at $4\text{km/h}$ in still water. If he is crossing a river when the speed of current is $2\text{km/h}$ , and if width of the river is $4\text{km}$, what is the minimum possible time?

• A. $1h$
• B. $0.5h$
• C. $\frac{2}{\sqrt{3}}h$
• D. $\sqrt{2}h$

Answer 1

The correct option is A $1h$

To cross the river in shortest time, velocity of boat w.r.t river must be perpendicular to the flow of river. Hence, for shortest time $\theta =0^{\circ }$, where $\theta$ is taken from the line perpendicular to the velocity of river.
$⟹t_{min}=\frac{w}{\left(v_{br}\cos 0^{\circ }\right)}=\frac{4}{4}=1h$
Hence, the minimum possible time required to cross the river is $1h$.