• # question_answer                 The speed of a boat is 5 km/h in still water. It crosses a river of width 1.0 km along the shortest possible path in 15 min. The velocity of the river water is: (in km/h)                     A)                 5        B)                 1              C)                                            3          D)                                            4

Correct Answer: C

Solution :

Let ${{v}_{r}}=$ velocity of river                 ${{v}_{br}}=$velocity of boat in still water and                 w = width of river                 Time taken to cross the river = 15 min                 $=\frac{15}{60}h=\frac{1}{4}\,h$                                 Shortest path is taken when ${{v}_{b}}$ is along AB. In this case                 $v_{br}^{2}=v_{r}^{2}+v_{b}^{2}$                 Now,     $t=\frac{w}{{{v}_{b}}}=\frac{w}{\sqrt{v_{br}^{2}-v_{r}^{2}}}$ $\therefore \frac{1}{4}=\frac{1}{\sqrt{{{5}^{2}}-v_{r}^{2}}}$ $\Rightarrow {{5}^{2}}-v_{r}^{2}=16$ $\Rightarrow v_{r}^{2}=25-16=9$ $\therefore {{v}_{r}}=\sqrt{9}\,=3\,km/h$                 Note:    If ${{v}_{r}}\ge {{v}_{br}}$, the boatman can never reach at point B.

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