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`
B. `t_2^2/t_1`
C. `sqrt(t_(1)t_(2))`
D. `(t_(1)+t_(2))`

Answer

A

Explanation

Let u be the velocity of swimmer and v be the velocity of river flow. Then
`t_(1)=(2d)/(sqrt(u^2-v^2))" "...(i)`
and `t_(2) = (d)/(u-v)+d/(u+v)=(2ud)/(u^2-v^2)" "...(ii)`
If t is the time taken by swimmer to swim a distance 2d in still
water , then `t = (2d)/u`
`:. t_(2)xxt=(2ud)/(u^2-v^2)xx(2d)/(u)=(4d^2)/(u^2-v^2)=t_1^2" "` (Using (i))
or `t =t_(1)^2/t_2`