Question

a swimmer can swim at 4 m per second in stillwater he has to cross a river of width 16 metre flowing with a speed of 3 metre per second then the minimum time in which he can cross the river is

Answer 1

Given:

A swimmer can swim at 4 m/s in stillwater he has to cross a river of width 16 metre flowing with a speed of 3 m/s.

To find:

Shortest time to cross the river.

Calculation:

In order to cross the river in shortest time the man has to swim perpendicular to the direction of river flow. But due to flow of water in the river the man will be drifted.

So , velocity of man w.r.t river will be :

$v = \sqrt{ {4}^{2} + {3}^{2} } = \sqrt{25}$

$= > v = 5 \: m {s}^{ - 1}$

So , the possible trajectory of the swimmer will be along line AC (refer to diagram) :

In ∆ABC :

$\sin( \theta) = \dfrac{3}{5}$

So, time taken be :

$\therefore \: t = \dfrac{AC}{v}$

$= > \: t = \dfrac{ \{\frac{AB}{ \cos( \theta)} \} }{v}$

$= > \: t = \dfrac{ \{\dfrac{16}{ \frac{4}{5} } \}}{5}$

$= > \:t = \dfrac{20}{5}$

$= > \:t = 4 \: sec$

So , final answer is :

Time taken is 4 seconds.