Question

A swimmer crosses a flowing stream of width 𝑤 to and fro in time $t_1$. The time taken to cover the same distance up and down the stream is $t_2$. If $t_3$ is the time the swimmer would take to swim a distance $2W$ in still water, then

• A. $t_3=t_1+t_2$
• B. $t_3^2=t_1{t}_2$
• C. $t_1^2=t_2{t}_3$
• D. $t_2^2=t_1{t}_3$

Answer 1

The correct option is C $t_1^2=t_2{t}_3$

Let $v$ be the river velocity and $u$ the velocity of swimmer in still water. Then

$t_1=2\left(\frac{W}{\sqrt{u^2-v^2}}\right)$

$t_2=\frac{W}{u+v}+\frac{W}{u-v}=\frac{2uW}{u^2-v^2}$

$t_3=\frac{2W}{u}$

Now we can see that $t_1^2=t_2{t}_3$

Correct option is (a).