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

Options

A. `pi//8`
B. `pi//6`
C. `pi//3`
D. `pi//4`

Answer

2

Explanation

`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`