Question

A boat having a speed of $5\text{km/h}$. in still water, crosses a river of width $1\text{km}$ along the shortest possible path in $15:\text{minutes}$. The speed of the stream in $\text{km/h}$

• A. $1$
• B. $3$
• C. $4$
• D. $\sqrt{41}$

Answer 1

The correct option is B $3$

$\text{Velocity of boat with respect to ground}=\frac{\text{Distance}}{\text{Time}}=\frac{1}{0.25}=4\text{km/h}$
$\text{Velocity of boat with respect to water}=5\text{km/h}$
$\text{Let velocity of water}=v\text{km/h}$
$5^2=4^2+v^2+2\times 4\times v\times \cos \theta$
$\text{Since boat travelled shortest path i.e. perpendicular, so}\theta ={90}^0$
$v^2=25-16$
$\Rightarrow v=3\text{km/h}$