Projectile Motion

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Range is maximum when launch angle is:

RankGuru · Accepted Answer

The horizontal range $R$ of a projectile is given by:
$R = \frac{u^2 \sin 2	heta}{g}$
To maximize $R$ for a given $u$, the term $\sin 2	heta$ must be maximum. 
The maximum value of the sine function is 1, which occurs when the angle is $90^\circ$.
$2	heta = 90^\circ \implies 	heta = 45^\circ$.
Thus, a launch angle of $45^\circ$ provides the maximum range on horizontal ground.

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