Question

a swimmer who can swim in a river with speed mv (with respect to still water) where v is the velocity of river current, jumps into the river from one bank to cross the river (give perfect solution i am giving 20 points for answer......imperfect answer will be deleted)

Answer 1

Given:

A swimmer who can swim in a river with speed mv (with respect to still water) where v is the velocity of river current, jumps into the river from one bank to cross the river.

To find:

Least time in which swimmer can cross the river.

Calculation:

Let width of river be L

Now , for least time , the swimmer has to jump perpendicularly to flow of river , but in course of time will get drifted.

Distance travelled will be :

$\therefore \: d = \dfrac{L}{ \cos( \theta) }$

$= > \: d = \dfrac{L}{ ( \frac{mv}{v \sqrt{ {m}^{2} + 1 } } ) }$

$= > \: d = \dfrac{L \sqrt{ {m}^{2} + 1} }{ m}$

Velocity of swimmer w.r.t river :

$\therefore \: v_{net} = \sqrt{ {(mv)}^{2} + {v}^{2} }$

$= > v_{net} = v \sqrt{ {m}^{2} + 1 }$

Hence , time taken is :

$= > \: t = \dfrac{(\frac{L \sqrt{ {m}^{2} + 1} }{ m}) }{v \sqrt{ {m}^{2} + 1} }$

$= > \: t = \dfrac{L}{mv}$

So , final answer is :

$\boxed{ \sf{ \: t = \dfrac{L}{mv} }}$

Answer 2

Answer:

l/mv is answer dear friend