Question

A man swims to and fro along the bank of a river with avelocity 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)u+v/2C) V square minus u square divided by 2​

Answer 1

Answer:

the average speed is $\frac{v^2-u^2}{v}$

Explanation:

Velocity of the man in w.r.t. to river = v

velocity of the flow = u

Velocity of the man downstream = v + u

Velocity of the man downstream = v - u

Let the distance is d

Tthen

Time taken to travel the distance d downstream = d/(v+u)

time taken to travel the distance d ustreapm = d/(v-u)

Total time = $\frac{d}{v+u}+\frac{d}{v-u}$

                 = $d(\frac{v-u+v+u}{v^2-u^2})$

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

Average speed = Total Distance/Total Time

                          = $\frac{2d}{\frac{2vd}{v^2-u^2}}$

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