Question

A swimmer can swim in still water at $ 1.5 m{s}^{-1}$. The river is flowing with $ 2 m{s}^{-1}$ from left to right. The minimum time taken by swimmer to cross the river and the drift in that case are respectively

1 iver flow V=2ms' d =200m

• A. $\left(\frac{20}{9}\right)minute$ ,$\left(\frac{800}{3}\right)m$
• B. $\left(\frac{10}{9}\right)minute$ ,$\left(\frac{400}{3}\right)m$
• C. $\left(\frac{40}{9}\right)minute$ ,$\left(\frac{200}{3}\right)m$
• D. $\left(\frac{5}{3}\right)minute$ ,$200m$

Answer 1

The correct option is A

$\left(\frac{20}{9}\right)minute$ ,$\left(\frac{800}{3}\right)m$

Step 1. Find the minimum time taken by swimmer to cross the river

It is given that Width of river $=200m$ and speed of swimmer $=1.5m{s}^{-1}$

The minimum time taken by the swimmer to cross the river $=\frac{\text{Width of the river AB}}{\text{speed of the swimmer}}$ $$\begin{gathered} =\frac{200}{1.5} \\ =\frac{400}{3}\text{seconds} \\ =\frac{400}{3x60}[\because 1\text{minute}=60\text{seconds}] \\ =\frac{20}{9}\text{minutes} \end{gathered}$$

Step 2. Find drift

Drift $=\text{speed of the river × time taken by swimmer to cross the road}$

$$\begin{gathered} =2\times \frac{400}{3}m \\ =\frac{800}{3}m \end{gathered}$$

Hence, option (A) is the correct option.