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 motion)is

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

Answer 1

The correct option is A $\frac{v^2-u^2}{v}$

Speed of river, $u$

Speed of man relative to water,$v$

Downward speed of man w.r.t ground, $v+u$

Upward speed of man w.r.t ground, $v-u$

Downward time, $t_1=\frac{s}{v+u}$and upward time $t_2=\frac{s}{v-u}$

Average speed = total distance/ total time

Average speed, $V_{av}=\frac{s+s}{\frac{s}{v+u}+\frac{s}{v-u}}=\frac{v^2-u^2}{v}$

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