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:

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) √uv (C) (u + v/2) (D) (v2 -u2/v)

Tardigrade Admin · Accepted Answer

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{2 d v}{v ^{2} - u ^{2}}

Average speed

= \frac{total distance}{total time}

= \frac{2 d}{t} = \frac{v ^{2} - u ^{2}}{v}

Q. 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:

0

$uv$

$\frac{u + v}{2}$

$\frac{v ^{2} - u ^{2}}{v}$

Q. 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:

0

uv​

2u+v​

vv2−u2​

Q. 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:

$uv$

$\frac{u + v}{2}$

$\frac{v ^{2} - u ^{2}}{v}$