1.

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

Answer»

`pi//8`
`pi//6`
`pi//3`
`pi//4`

Solution :`TAN theta = tan (theta_(2)-theta_(1))`
`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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