Relation in Projectile Motion

Relation between horizontal range and maximum height of a Projectile

The relation between the range  R  on the horizontal plane and the maximum height  h  reached at  \frac{t_d}{2}  is:
h = \frac{R\tan\theta}{4}

Proof

h = \frac{v_0^2\sin^2\theta}{2g}
R = \frac{v_0^2\sin2\theta}{g}
\frac{h}{R} = \frac{v_0^2\sin^2\theta}{2g}  ×  \frac{g}{v_0^2\sin2\theta}
\frac{h}{R} = \frac{sin^2\theta}{4sin\theta\cos\theta}
h = \frac{R\tan\theta}{4}
(This is originally edited by Saisundar for wiki)
For details refer Wiki pedia

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