Q. A swimmer crosses a flowing stream of width ‘d’ to and fro normal to the flow of the river in time t1. The time taken to cover the same distance up and down the stream is t2. If t3 is the time the swimmer would take to swim a distance 2d in still water, then relation between t1, t2 & t3.
(a) $\displaystyle t_1 = \sqrt{t_2 t_3} $
(b) $ \displaystyle t_1 = \sqrt{t_2 / t_3} $
(c) $ \displaystyle t_1 = \sqrt{t_3 / t_2} $
(d) $ \displaystyle t_1 = t_3 t_2 $
Click to See Answer :
Sol: Let u = velocity of swimmer in still water
v = velocity of river flow
$ \displaystyle t_1 = 2 (\frac{d}{\sqrt{u^2-v^2}} ) $ …(i)
$ \displaystyle t_2 = \frac{d}{u+v}+\frac{d}{u-v} $ …(ii)
$\displaystyle t_3 = \frac{2 d}{u} $ …(iii)
On multiplying (ii) and (iii) we get
$ \displaystyle t_2 \times t_3 = t_1^2 $
$ \displaystyle t_1 = \sqrt{t_2 t_3} $