Question

Two men who can swim with a speed $v_1$ in still water start from the middle of a river of width d and move in opposite directions always swimming at an angle $\theta$ with the banks. What is the distance between them along the river when they reach the opposite banks, if the velocity of the river is $v_2$

• A. $\frac{d{v}_1}{d{v}_2}cot\theta$
• B. $\frac{d{v}_{1}cos\theta }{v_1+v_2}$
• C. $\frac{d{v}_1}{v_1}tan\theta$
• D. $\frac{v_{2}d}{v_{1}sin\theta }$

Answer 1

The correct option is D

$\frac{v_{2}d}{v_{1}sin\theta }$

$t_1=\frac{\frac{d}{2}}{v_{1}sin\theta }$
Distance $=\left\{\right(v_2+v_{1}cos\theta )+(v_2-v_{1}cos\theta \left)\right\}\frac{d}{2v_{1}sin\theta }$
$=\frac{v_{2}d}{v_{1}sin\theta }$