Two particles A and B are projected from the same point with the same velocity of projection but at different angles `alpha `and `beta` of projection, such that the maximum height of A is two-third of the horizontal range of B. then which of the following relations are true?

Options

A. `3(1-cos 2alpha)=8sin 2beta`
B. Range of A=maximum height of B
C. Maximum vlaue of `beta` is `(1)/(2)sin^(-1)(3)/(4)`
D. Maximum horizontal range of A `=(u^(2))/(g)` and this occurs when `beta=(1)/(2)sin^(-1)(3)/(8)`

Answer

a,c,d

Explanation

`(u^(2)sin^(2)alpha)/(2g)=(2)/(3)(u^(2)sin 2beta)/(g)`
`sin^(2)alpha=(4)/(3)xx2sin beta.cosbeta`
`((1-cos2alpha))/(2)=(4)/(3) sin 2beta`
`beta_("max")=sin^(-1)((3)/(4))`