A man crosses a river in a boat. If he crosses the river in minimum time he takes 10 minutes with a drift 120m. If he crosses the river taking shortest path, he takes 12.5 minute, find
(i) width of the river, (ii) velocity of the boat with respect to water, (iii) speed of the current.
Assume $v_{b / r} > v_{r}$

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Solution

$v e l o c i t y o f t h e r i v e r = \frac{d r i f t d u r i n g t h e m i n i m u m t i m e}{t i m e} = \frac{120 m}{10 m i n} = 12 m / m i n \frac{d}{v_{b / r} c o s θ} = 12.5 a n d v_{b / r} s i n θ = 12 a n d \frac{d}{v_{b / r}} = 10 v_{b / r} = 20 m / m i n d = 200 m$

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