The path traveled by an object (neglecting air resistance) that is projected at an initial height of h0 feet, an initial velocity of v0 feet per second, and an initial angle is given by

where the horizontal distance x and the vertical distance y are measured in feet. Find a formula for the maximum height of an object projected from ground level at velocity v0 and angle θ. To do this, find half of the horizontal distance 1 / 32 v02 sin 2θ and then substitute it for x in the model for the path of a projectile (where h0 = 0).

16 x + (tan 0)x + ho y = v cos? 0*