A man swims to and fro along the bank of a river with a velocity `v` relative to water. If the velocity of flow is `u`, the average speed of the man (for to and fro motion) is :

Options

A. 0
B. `sqrt(u v)`
C. `(u + v)/(2)`
D. `(v^2 - u^2)/(v)`

Answer

D

Explanation

Velocity of man relative to ground in upstream
=`v - u`
where v = velocity of man relative to water
u = velocity of water flow
velocity of man relative to ground in downstream
Time taken to cover distance `d` into & from motion
`t = (d)/(v - u) + (d)/(v + u) = (2 dv)/(v^2 - u^2)`
Average speed `= ("total distance")/("total time")`
=`(2d)/(t) = (v^2 - u^2)/(v)`.