Question

A man wishes to cross a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift of $120$ m. If he crosses the river taking shortest route, he takes $12.5$ minutes. Find velocity of the boat with respect to water.

• A. 20 m/min
• B. 12 m/min
• C. 10 m/min
• D. 8 m/min

Answer 1

Answer: (A)

$10=\frac{L}{v}$ (i)
$12.5=\frac{L}{\sqrt{v^2-u^2}}=\frac{L}{v\sqrt{1-u^2/v^2}}$ (ii)
From (i) and (ii) $\frac{1}{12.5}=\frac{L}{v}\times \frac{v\sqrt{1-u^2/v^2}}{L}$
$\frac{4}{5}=\sqrt{1-\frac{12^2}{v^2}}$
$\frac{16}{25}=1-\frac{12^2}{v^2}$
$\Rightarrow \frac{12^2}{v^2}=1-\frac{16}{25}=\frac{9}{25}$
$\frac{12}{v}=\frac{3}{5}$
$\Rightarrow v=\frac{12\times 5}{3}=20m/s$