Question

A swimmer crosses a flowing stream of width $\omega$ 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 $2\omega$ in still water, then

• A. $t_{1}^{2}=t_{2}t_{3}$
• B. $t_{2}^{2}=t_{1}t_{3}$
• C. $t_{2}^{3}=t_{1}t_{2}$
• D. $t_{3}=t_{1}+t_{2}$

Answer 1

Answer: (A)

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) $
$t_{2}=\frac{W}{u+v}+\frac{W}{u-v}=\frac{2uW}{u^{2}-v^{2}} \,\,and \,\,t_{3} = \frac{2W}{u}$
Now we can see th $t^{2}_{1}=t_{2}t_{3}$