Question

A boat which has a speed $5\text{km/h}$ in still water crosses a river of width $100\text{m}$ along the shortest possible path in $1.5\text{min}$. The velocity of river water in $\text{km/h}$ is

• A. $1$
• B. $3$
• C. $4$
• D. $4.1$

Answer 1

The correct option is B $3$

For shortest path velocity diagram is as shown
Given velocity of boat in still water $v_{bw}=5\text{km/h}$
let $v_b$ be velocity of boat, $v_w$ be velocity of water
Now time taken for boat to cross the river is $t=1.5\text{min}=\frac{w}{v_b}=\frac{100}{v_b}$
$v_b=\frac{100}{1.5}\frac{\text{m}}{\text{min}}$

$v_b=\frac{100}{1.5}\times \frac{1}{1000}\times 60\text{km/h}$
$v_b=4\text{km/h}$

Using pythagoras theorem
$\Rightarrow v_w=\sqrt{v_{bw}^2-v_b^2}=\sqrt{5^2-4^2}$
$\Rightarrow v_w=3\text{km/h}$