A swimmer crosses a flowing stream of width `d` to and fro normal to the flow of the river at 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 relation between `t_(1),t_(2)`&`t_(3)`.

Options

A. `t_(1)^(2)=t_(2)t_(3)`
B. `t_(2)^(2)=t_(1)t_(3)`
C. `t_(3)^(2)=t_(1)t_(2)`
D. `t_(3)=t_(1)+t_(2)`

Answer

a

Explanation

Let v be the river velocity and u the velocity of swimmer in still water. Then
`t_(1)=2(W/(sqrt(u^(2)-v^(2))))`
`t_(2)=W/(u+v)+W/(u-v)=(2uW)/(u^(2)-v^(2)) and t_(3)=(2W)/u`
Now we can see that `t_(1)^(2)=t_(2)t_(3)`