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JCECE Medical JCECE Medical Solved Paper-2013

  • question_answer
    A boat can go across a lake and return in time \[{{T}_{0}}\]at a speed \[\upsilon .\]On a rough day there is a uniform current at speed \[{{\upsilon }_{1}}\] to help the onward journey and impede the return journey. If the time taken to go across and return on the same day be T, then \[T/{{T}_{0}}\]will be

    A) \[\frac{1}{(1-v_{1}^{2}/{{v}^{2}})}\]

    B)  \[\frac{1}{(1+v_{1}^{2}/{{v}^{2}})}\]

    C)  \[(1-v_{1}^{2}/{{v}^{2}})\]

    D)  \[\left( 1+\frac{v_{1}^{2}}{{{v}^{2}}} \right)\]

    Correct Answer: A

    Solution :

    Let d be the width of lake to be crossed then \[{{T}_{0}}=\frac{2d}{v}\] and \[T=\frac{d}{(v+{{v}_{1}})}-\frac{d}{(v-{{v}_{1}})}\] \[=\frac{2d\,v}{{{v}^{2}}-v_{1}^{2}}\] \[=\frac{2dv}{{{v}^{2}}(1-v_{1}^{2}/{{v}^{2}})}\] \[=\frac{2d}{v(1-v_{1}^{2}/{{v}^{2}})}\] So, \[\frac{T}{{{T}_{0}}}=\frac{1}{(1-v_{1}^{2}/{{v}^{2}})}\]


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