Finding the optimal launch for a projectile?

1. Sep 26, 2014

Boatman(J)

Suppose I wanted to launch a water balloon off a cliff of a known height of H and known initial Velocity of Vo, where we can neglect air resistance. Using Newton's Second Law and differentiating it, how can i derive an equation for maximum distance traveled (xmax) at an angle theta? Then from the equation derived for xmax, how can I create another equation that can be use to derive the optimal angle which allows the ballon to travel the xmax? I will then use that equation for the optimal angle to find the optimal angle by root finding with the use of fzero in matlab.

I did this through kinematics but it was done wrong and kept telling me that optimal angle was 89 degress.