A swimmer crosses a flowing stream 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 n

A swimmer crosses a flowing stream of width .d. to and fro in time t_(

1.	A swimmer crosses a flowing stream 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 n
Answer» SOLUTION :Let v be the RIVER VELOCITY and u the velocity of swimmer in STILL water. Then `t_(1)=2((d)/(SQRT(u^(2)-v^(2))))…….(i)` `t_(2)=(d)/(u+v)+(d)/(u-v)=(2ud)/(u^(2)-v^(2))…..(ii)` and `t_(3)=(2d)/(u)…….(iii)` from equation (i), (ii) and (iii) `t_(1)^(2)=t_(2)t_(3)=sqrt(t_(2)t_(3))`