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  4. 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.

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Q. 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.

Motion in a Plane

Solution:

image
$10= \frac{L}{v}$ (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} $
$\Rightarrow v = \frac{12 \times 5}{3} = 20\,m/s$