Question

A boat can row with a speed of $10km/hr$ in still water. The river flows steadily at $5km/hr$ and the width of the river is $2km$. If the boat man cross the river with reference to minimum distance of approach then time elapsed in rowing the boat will be

• A. $\frac{2\sqrt{3}}{5}hr$
• B. $\frac{2}{5\sqrt{3}}hr$
• C. $\frac{3\sqrt{2}}{5}hr$
• D. $\frac{5\sqrt{2}}{3}hr$

Answer 1

The correct option is B $\frac{2}{5\sqrt{3}}hr$

$\overrightarrow{V_{br}}=\overrightarrow{V_b}-\overrightarrow{V_r}$

Using pythagoras theorem Vb=Vbr2−Vr2V_{b}=\sqrt{V_{\text{br}}^2 -V_r^2}Vb​=Vbr2​−Vr2​​

Time taken,
$t=\frac{d}{\sqrt{V_{\text{br}}^2-V_r^2}}=\frac{2}{\sqrt{{10}^2-5^2}}=\frac{2}{5\sqrt{3}}\text{hrs}$