NEET Sample Paper NEET Sample Test Paper-21

  • question_answer A boat crosses a river from point A to point B, which are on opposite sides. The speed of water is v and that of boat is \[{{v}_{w}}\]relative to still water. Assume\[{{v}_{B}}=2{{v}_{w}}.\]What is the time taken by the boat to cross the river, if the width of the river is D

    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 :

    Where b is the velocity of boat with respect to ground Let the time to cross the river bet t \[t=\frac{D}{v}=\frac{D}{\sqrt{v_{B}^{2}-v_{w}^{2}}}=\frac{D}{\sqrt{v_{B}^{2}-{{\left( \frac{{{v}_{B}}}{2} \right)}^{2}}}}\] \[\therefore \]    \[t=\frac{2D}{{{v}_{B}}\sqrt{3}}\] Hence, the correction option is (a).


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