|I don't understand the horizontal component of a ball thrown downfield. Does it have constant velocity and/or acceleration, even at the start?
Until you let go of the ball, you are in control of its velocity and acceleration. During that time, it does accelerate and its velocity isn't constant. But as soon as you let go of the ball, everything changes. The ball's motion in flight can be broken up into two parts: its vertical motion and its horizontal motion. Horizontally, the ball travels at a constant speed because there is nothing pushing or pulling on it horizontally (neglecting air resistance). Vertically, the ball accelerates downward at a constant rate because gravity is pulling down on it. Thus the ball travels steadily forward in the horizontal direction as it fall in the vertical direction. Of course, falling can begin with upward motion, which gradually diminishes and is replaced by downward motion.