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Two runner A and B start at the origin and run along positive x axis ,with B running three times as fast as A. An obsever, standeing one unit above the origin , keeps A and B in view.Then the maximum angle theta of sight between the observer's view of A and B is |
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Answer» `pi//8` `RARR tan theta =(3x-x)/(1+3xx)=(2x)/(1+3x^(2))` `Let y=(2x)/(1+3x^(2))` `rarr (dy)/(dx)=2(1-3x^(2))/(1+3x^(2^(2)))` and `(d^(2)y)/(dx^(2))=(-24x)/(1+3x^(2^(3)))lt0 for x =1//sqrt(3)` `therefore theta_(MAX)=pi//6` |
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