A stone projected with a velocity u at an angle $\theta$ with the horizontal reaches maximum height $H_1$. When it is projected with velocity u at an angle $\left( {\frac{\pi }{2} - \theta } \right)$ with the horizontal, it reaches maximum height $ H_2$. The relation between the horizontal range R of the projectile, $H_1$ and $H_2$ is

  • A

    $R = 4\sqrt {{H_1}{H_2}} $

  • B

    $R = 4({H_1} - {H_2})$

  • C

    $R = 4({H_1} + {H_2})$

  • D

    $R = \frac{{{H_1}^2}}{{{H_2}^2}}$

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