A swimmer wishes to cross a $500 m$ wide river flowing at $5 K m / h$ . His speed with respect to water is $3 K m / h$ .
Find the shortest possible time to cross the river.

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Solution

a) vertical component to opposite side is $3 s i n θ$
Distance = $0.5 k m$
velocity = $3 s i n θ$

Time = $\frac{D i s t a n c e}{V e l o c i t y}$

= $\frac{0.5}{3} s i n θ$ sec

= $\frac{10}{s i n θ}$ min.

b) vertical component to opposite side = $3 k m / h r$
Time = Distance/Velocity
= $\frac{0.5}{3}$
= $0.16 h r$
Converting into min: 0.16 hr = 60 x 16 = 9.6 or 10 minute.

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