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Discussion Response Post to: HeLp PLZ

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anchit saini (4396)

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$Let \ CD =x \\ \\ Speed \ of \ car \ in \ field = v \\ \\ Speed \ of \ car \ in \ highway = \eta v \\ \\ t_1= \mbox{time taken to cover AC} = \frac{d - x}{\eta v} \\ \\ t_2= \mbox{time taken to cover CB} = \frac{\sqrt{l^2 + x^2}}{v}\\ \\ t= t_1 + t_2 \\ \\ \mbox{For t to be minimum }\frac{dt}{dx}=0 \\ \\ or \\ \\ \frac{-1}{\eta} + \frac{x}{\sqrt{l^2 +x^2}}=0 \\ \\ which \ gives \\ \\ x=\frac{l}{\sqrt{\eta ^2 - 1}}$

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