Question

A man is crossing a river flowing with a velocity of $5m/s$. He reaches a point directly across the distance is $60m$ in $5$ seconds. His velocity in the still water should be

• A. $13m/s$
• B. $12m/s$
• C. $10m/s$
• D. $5m/s$

Answer 1

The correct option is A

$13m/s$

Step 1: Given

The velocity of man in the flowing river: $v=5m/s$

Distance travelled by man: $d=60m$

Time taken to travel: $t=5s$

The velocity of man in still water: $u=?$

Step 2: Formula used

Time taken to cross a river using the shortest path is given by

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

Where, $d$ is the distance travelled, $u$ is the velocity in still water and $v$ is the velocity in flowing river

Step 3: Substitute the values in the given formula and find the value of u

$$\begin{gathered} 5=\frac{60}{\sqrt{5^2-u^2}} \\ \Rightarrow \sqrt{25-u^2}=\frac{60}{5} \end{gathered}$$

Square both sides and find the value of u:

$$\begin{gathered} 25-u^2=144 \\ \Rightarrow u^2=144+25=169 \\ \Rightarrow u=13m/s \end{gathered}$$

Hence, option (A) is the correct answer.