Question

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:

• A. 0
• B. $\sqrt{uv}$
• C. $\frac{u + v}{2}$
• D. $\frac{v^2 -u^2}{v}$

Answer 1

Answer: (D)

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 $d$ in to & from motion
$t = \frac{d}{v -u} + \frac{d}{v + u} =\frac{2dv}{v^2 - u^2}$
Average speed $= \frac{\text{total distance}}{\text{total time}}$
$= \frac{2d}{t} = \frac{v^2 -u^2}{v}$