Question

A swimmer can swim with speed 'V' with respect to still water in a river which is flowing with speed u. There a float moving with the river, Now the swimer float and gets a lead lot $\ell$ and returns back to the float . Time taken by swimer in this process will be

• A. $\frac{2\ell }{v}$
• B. $\frac{2\ell }{u}$
• C. $\frac{\ell }{\sqrt{v^2-u^2}}$
• D. $\frac{\ell }{V+u}+\frac{\ell }{V-u}$

Answer 1

The correct option is A $\frac{2\ell }{v}$

Float will move with the speed of river, so speed of float $=u$

When swimmer gets a lead of $l$, it will swim downstream with velocity $=V+u$

Relative velocity of swimmer with respect to float $=(V+u)-u=V$

Time taken by swimmer $=\frac{l}{V}$

Now for return swimmer will swim upstream with velocity$=V-u$

Both are moving in opposite direction with, so relative velocity of swimmer with respect to float $=V-u-(-u)=V$

Time taken by swimmer for return $=\frac{l}{V}$

Total time taken $=\frac{2l}{V}$