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 \[(\frac{\pi }{2}-\theta )\] 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. \[R=\,\frac{{{H}^{2}}_{1}}{{{H}^{2}}_{2}}\]