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Relative Velocity

A man can swi...

Question

A man can swim in still water at a speed of $3 k m / h$ . He wants to cross a river that flows at $2 k m / h$ 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 body makes with the river flow)?
(b) How much time will he take to cross the river if the river is $500 m$ wide?

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Solution

Angle, $α$ = $θ + 90$
Velocity of man is still river $V_{M R}$ = $3 K m / h r$
$V_{M R} sin θ = V_{R}$ if the man wants no deflection
$\begin{matrix} ∴ sin θ = \frac{2}{3} sin (α - 90) = \frac{2}{3} cos α = \frac{- 2}{3} α = {cos}^{- 1} (\frac{- 2}{3}) {\to V}_{M} = {\to V}_{M R} + {\to V}_{R} N o w, {\to V}_{M} ⊥ {\to V}_{R} V_{M} = V_{M R} cos θ = 3 \times \frac{\sqrt{5}}{3} = \sqrt{5} k m / h t = \frac{500 m}{V_{M}} = \frac{0.5 k m}{V_{M}} = \frac{0.5}{\sqrt{5}} h r s = 0.1 \times \sqrt{5} h r \end{matrix}$

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