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  • A man starting from point P crosses a 4 km wide lagoon and reaches point Q in the shortest possible time by the path shown. If the person swims at a speed of 3 km/hr and walks at a speed of 4 km/hr

A man starting from point P crosses a 4 km wide lagoon and reaches point Q in the shortest possible time by the path shown. If the person swims at a speed of 3 km/hr and walks at a speed of 4 km/hr, then his time of journey is \left(\mu_{\text {salt water }}=4 / 3\right) \text { : }

Option: 1

4hr, 10 min


Option: 2

4 hr and 30 min


Option: 3

3 hr and 50 min


Option: 4

5 hr and 10 min


Answers (1)

best_answer

As we know that light travels in a path such as to reach from one point to another in shortest possible time.

Therefore, the man must travel along that path on which light would have travelled in moving from P to Q.

\mathrm{ \text { By Snell's law; } \frac{\sin i}{\sin r}=\frac{\mu_2}{\mu_1} \\ }

\mathrm{ \sin r=\frac{\mu_1}{\mu_2} \cdot \operatorname{sin~i} \\ }

\mathrm{ \sin r=\frac{3}{5} \cdot \frac{4}{3}=\frac{4}{5} \Rightarrow r=53^{\circ} \\ }

\mathrm{ \therefore \quad A Q=10 \mathrm{~Km} . }

\mathrm{From ~P ~to ~A: t_1=\frac{5}{3} }

\mathrm{From ~A ~to ~Q: t_2=\frac{10}{4}=\frac{5}{2} }

\mathrm{ \mathrm{T}=\mathrm{t}_1+\mathrm{t}_2=\frac{5}{3}+\frac{5}{2}=\frac{25}{6} \mathrm{hr} \\ }

\mathrm{ =\left(\frac{24}{6}+\frac{1}{6}\right) \mathrm{hr}=\left(4 \mathrm{hr}+\frac{1}{6} \mathrm{hr}\right)=4 \mathrm{hr}+10 \text { minutes } }
 

Posted by

Ajit Kumar Dubey

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