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Crossing the River(Minimum Time)

2 km wide riv...

Question

$2 k m$ wide river flowing at the rate $5 k m / h r$ . A man can swim is still water $10 k m / h r$ . He wants to cross the river along the shorted path. Find-
(a) in which direction should the person swim.
(b) crossing time.

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Solution

Since the man goes along the shortest path.
So, $10 cos θ = 5$
$cos θ = \frac{1}{2}$
$θ = 60^{o}$ from opposite to flow
or $θ = 180 - 60$ from flow
$= 120^{o}$
Time taken $= \frac{d i s t a n c e}{s p e e d} = \frac{2}{10 sin 60}$
$= \frac{1}{5 \times \frac{\sqrt{3}}{2}}$
$= \frac{2}{5 \sqrt{2}}$

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