A man can swim in still water at a speed of 3 km/h. he want to cross a river that flows at 2 km/h and reach the point directly opposite to his starting point. (a) In which direction should he try to swim (that is, find the angle his bodys makes with the river flows)? (b) How much time will he take to cross the river if the is 500 m wide ?

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Solution

swimming speed of man is $3 k m / h$ .

river flow speed is $2 k m / h$ .

To reach the point directly opposite to his stating point.
$sin θ = 2 / 3$

$θ = {sin}^{- 1} (\frac{2}{3})$

$θ = {41.7}^{\circ}$

As the man has to reach directly of opposite to his stating point
then the angle has to lre. $90 + θ .$

$∴$ Required angle is $90 + θ = {131.7}^{\circ}$

$90 + 41.7 = 131.7$

(b) time to cross the rived is .

$T = \frac{d i s t a n c e}{s p e e d} = \frac{500 \times 10^{- 3}}{\sqrt{5}} = \frac{500 \times 10^{- 3}}{\sqrt{5}} \times \frac{\sqrt{5}}{\sqrt{5}}$
(speed of man w.r.t rives)

$T = \sqrt{5} \times 100 \times 10^{- 3} = 0.1 \times \sqrt{5}$ hours.

$T = 13.4$ minutes.

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