A particle is projected from the ground so as to graze the four upper vertices of a regular hexagor, whose side is 2a and which is placed vertically with one side on the ground.

What is the range on the ground.

Options

A. `3sqrt(7a)`
B. `sqrt(7a)`
C. `2sqrt(7a)`
D. `3a`

Explanation

`x_(0)=(R(4a cos 60^(@)+2a))/(2)`
`x_(0)=(R)/(2)-2a`
`y=tan thetax(1-(x)/(R))`
`asqrt(3)=tantheta x[(1-((R)/(2)-2a))/(R)]`
`2asqrt(3)=tan theta[((R)/(2)-2x)]+2a cos 60^(@)[1-((R)/(2)-2a+a)/(R)]`
`(1)/(2)=((R-4a))/(R-2a)([R-(R)/(2)+2a])/([R-(R)/(2)a])=((R-4a))/(((P,-2a)))`
`([R+4a])/((R+2a))`
`(1)/(2)=(R^(2)-16a^(2))/(R^(2)-4a^(2))`
`R^(2)-4a^(2)=4R^(2)-32a^(2)`
`R=2a sqrt(7)`