At what angle of projection is the range maximum? Prove it mathematically.
To solve for the required angle of projection ( ), we need first to find a general expression for the range.
To find range, set y = 0 first and use:
,
Solving for the general expression for range,
Regardless of the value of , the maximum value of range would be attain if
is maximum. Since 1 is the maximum value of sine function, then,
should be equal to 1. Since sin 90º = 1, therefore
(angle of projection) should be equal to 45º
