The trajectory of a projectile in a vertical plane is y = $\alpha$x $-$ $\beta$x2, where $\alpha$ and $\beta$ are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained H are respectively given by :

Question

The trajectory of a projectile in a vertical plane is y = $\alpha$x $-$ $\beta$x², where $\alpha$ and $\beta$ are constants and x & y are respectively the horizontal and vertical distances of the projectile from the point of projection. The angle of projection $\theta$ and the maximum height attained H are respectively given by :

${\tan ^{ - 1}}\alpha ,{{{\alpha ^2}} \over {4\beta }}$

${\tan ^{ - 1}}\alpha ,{{4{\alpha ^2}} \over \beta }$

${\tan ^{ - 1}}\left( {{\beta \over \alpha }} \right),{{{\alpha ^2}} \over \beta }$

${\tan ^{ - 1}}\beta ,{{{\alpha ^2}} \over {2\beta }}$

Solution

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