Question

A swimmer wishes to cross a $800\text{m}$ wide river flowing at $6\text{km/hr}$. His speed with respect to water is $4\text{km/hr}$. He crosses the river in shortest possible time. He is drifted downstream on reaching the other bank by a distance of

• A. $800\text{m}$
• B. $1200\text{m}$
• C. $400\sqrt{13}\text{m}$
• D. $2000\text{m}$

Answer 1

The correct option is B $1200\text{m}$

We know that, for the swimmer to cross the river in the shortest time,

$t=\frac{d}{v_m}=\frac{0.8}{4}=0.2\text{hr}$,

where,
$d=$ width of the river
$v_m=$ speed of the swimmer with respect to water

Hence the drift will be,

$\Delta x=v_r\times t=6\times 0.2=1.2\text{km}=1200\text{m}$

Hence, option $\left(\text{B}\right)$ is the correct answer.