Question Number 14920 by Tinkutara last updated on 05/Jun/17

A swimmer crosses a flowing river of width d 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 2d in still water, then prove that t_1 ^2 = t_2 t_3 .

Answered by ajfour last updated on 05/Jun/17

Commented byajfour last updated on 05/Jun/17

to go to the other bank and return back to same point (to and fro) swimmer must swim at an angle θ (see fig.) such that vsin 𝛉=u ...(i) t_1 =((2d)/(vcos 𝛉)) ....(ii) to go upstream a distance d and return back time taken is t_2 =(d/(v−u))+(d/(v+u)) ....(iii) to swim a distance 2d in still water time taken is t_3 =((2d)/v) . t_2 t_3 =((2d^2 )/v)(((2v)/(v^2 −u^2 ))) =((4d^2 )/(v^2 −v^2 sin ^2 θ)) = (((2d)/(vcos θ)))^2 = t_1 ^2 [see (ii), (iii), and (i) ].

Commented byTinkutara last updated on 05/Jun/17

Thanks Sir!