Question

A river $5\text{km}$ wide is flowing at the rate of $2\text{km/hr}$. The minimum time taken by a boat to cross the river with a speed $5\text{km/hr}$ (in still water) is approximately

• A. $150\text{min}$
• B. $300\text{min}$
• C. $60\text{min}$
• D. $90\text{min}$

Answer 1

The correct option is C $60\text{min}$

The minimum time is taken when the velocity of the boat with respect to the river is perpendicular to the direction of the river's flow. Then the vertical component of velocity of the boat is $5\text{kmph}$
Hence the minimum time taken to cross the river is
$t=\frac{d}{v_m}=\frac{5}{5}=1\text{hr}=60\text{min}$