Two particle are projected from an incliend plane as shown. A is projected up the incline and `B` down the incline. If `R_(A)` and `R_(B)` are range of `A` and `B` respectively then `(R_(B))/(R_(A))` will be equal to :

Options

A. `(3sqrt(3)+4)/(3sqrt(3)-4)`
B. `(3sqrt(3)-4)/(3sqrt(3)+4)`
C. `(3sqrt(3)+2)/(3sqrt(3)-2)`
D. `(4+sqrt(3))/(4-sqrt(3))`

Answer

D

Explanation

Two particle ……………
`(R_(A))/(R_(B)) = (cos(theta-phi))/(cos(theta+phi)) = ((4)/(5)xx(sqrt(3))/(2)+(3)/(5)xx(1)/(2))/((4)/(5)xx(sqrt(3))/(2)-(3)/(5)xx(1)/(2))=(4sqrt(3)+3)/(4sqrt(3)-3)`
`= (4+sqrt(3))/(4-sqrt(3))`