A projectile launched from and returning to the floor beneath a horizontal ceiling of height has maximum projectile range when . For higher ceilings the maximum is . This assumes uniform gravitational acceleration, no air resistance and fixed launch speed .
Indeed, with , the apex condition is and . This concave quadratic function is maximized at the admissible value nearest . Thus the lower-ceiling expression must not be extrapolated past its regime. If touching the ceiling is excluded, the limiting value is a supremum instead of an attained maximum.