NEET Sample Paper NEET Sample Test Paper-50

  • question_answer 16) A boat crosses a river from port A to port B, which are just on the opposite side. The speed of the water is \[{{V}_{W}}\] and that of boat is \[{{V}_{B}}\] relative to still water. Assume\[{{V}_{B}}=2{{V}_{W}}\]. What is the time taken by the boat, if it has to cross the river directly on the AB line?

    A) \[\frac{2D}{{{V}_{B}}\sqrt{3}}\]                      

    B) \[\frac{\sqrt{3}D}{2{{V}_{B}}}\]

    C) \[\frac{D}{{{V}_{B}}\sqrt{2}}\]                        

    D) \[\frac{D\sqrt{2}}{{{V}_{B}}}\]

    Correct Answer: A

    Solution :

    From figure, \[{{V}_{B}}\text{ }sin\,\theta \,\,=\,\,{{V}_{W}}\]   \[\sin \,\theta \,=\,\frac{{{V}_{W}}}{{{V}_{B}}}\,=\,\frac{1}{2}\,\,\Rightarrow \,\,\theta =30{}^\circ \,\,\,\,\,\,\,\,\,\,[\because \,\,{{V}_{B}}=2{{V}_{W}}]\] Time taken to cross the river, \[t=\frac{D}{{{V}_{B}}\cos \,\theta }=\frac{D}{{{V}_{B}}\,\cos \,30{}^\circ }=\frac{2D}{{{V}_{B}}\,\sqrt{3}}\]

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