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# Solve the following :

Question:

A swimmer wishes to cross $500 \mathrm{~m}$ wide river flowing at $5 \mathrm{~km} / \mathrm{h}$. His speed with respect to water is 3 $\mathrm{km} / \mathrm{h}$.

(a) If he heads in a direction making an angle $\theta$ with the flow, find the time he takes to cross the river.

(b) Find the shortest possible time to cross the river.

Solution:

(a) Velocity responsible for $\operatorname{cros} \operatorname{sing}=3 \sin \theta \mathrm{kmph}$

$=3 \times \frac{5}{18} \sin \theta$

Time to cross= $=\frac{\text { distance }}{\text { speed }}$

$=\frac{500 \times 18}{3 \times 5 \sin \theta}=\frac{600}{\sin \theta}$

$=\frac{10}{\sin \theta}$ minutes

(b) For $t_{\min } ; \sin \theta=1$

When $\theta=90^{\circ}$

$t_{\min }=10$ minutes