A ball being thrown, ignoring drag or wind, has an initial height, initial velocity, and experiences the acceleration due to gravity. When a ball is launched from the ground, y_0 = zero, complementary angles (for example 20 and 70 degrees) will produce the same distance for the same initial velocity, and the maximum distance is acheived at 45 degrees. However, with an initial height an angle of more than 45 degrees will result in a farther distance. My question then is what is the relationship between angle of trajectory and initial height to give the farthest distance for a constant velocity. It seems like there must be one... i've been drawing some graphs to try to figure it out. The time for the ball to reach maximum height will stay the same for every angle, and i think total travel time (counting the negative time) will be the same as well... Pretty curious, let me know what you think.