The trajectory of a projectile in a vertical plane is $y =\alpha x -\beta x ^{2},$ 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 :-
The trajectory of a projectile in a vertical plane is $y =\alpha x -\beta x ^{2},$ 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 :-
- [JEE MAIN 2021]
- A
$\tan ^{-1} \alpha, \frac{\alpha^{2}}{4 \beta}$
- B
$\tan ^{-1} \beta, \frac{\alpha^{2}}{2 \beta}$
- C
$\tan ^{-1} \alpha, \frac{4 \alpha^{2}}{\beta}$
- D
$\tan ^{-1}\left(\frac{\beta}{\alpha}\right), \frac{\alpha^{2}}{\beta}$
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