A projectile is required to hit a target whose co-ordinates relative to horizontal and vertical axes through the point of projection are `(alpha, beta)` If the projection speed is `sqrt(2g alpha)`. Then the condition when it is impossible to hit the target is

Options

A. `3alphagt4beta`
B. `3betagt4alpha`
C. `4alphagt3beta`
D. `4betagt3alpha`

Explanation

`beta=alpha tan theta-(1)/(2)g(alpha^(2))/(u^(2) cos^(2) theta)`,
`beta= alpha tan theta-(1)/(2)g(alpha^(2))/(2galpha)(1+tan^(2)theta)`,
`tan^(2)theta-4tan theta+(1+(4beta)/(alpha))=0`
If particle will not hit the target
`(b^(7)-4ac)lt0, 16-4(1+(4beta)/(alpha))lt0`
`4betagt3alpha`