Try this to help understand the bouncing ball:

    On your airplane's instrument panel, install a map, a velocity gauge, and an acceleration gauge.
    The map is fairly familiar: it shows where you are (but includes elevation).  The velocity gauge is not familiar (those are speed gauges!):  it's an arrow in three dimensions which shows both magnitude and direction of motion (that is, it shows velocity).
    Now here's where you need to stretch your insight a bit: the acceleration gauge.  Just as velocity is the rate of change of position, acceleration is the rate of change of velocity.  It, too, is a three-dimensional arrow and looks a lot like the velocity gauge.  The direction of the acceleration is the direction of motion of the tip of the arrow in the velocity gauge.
    Imagine you are in a car driving at constant speed on a straight stretch of road.  The car has a velocity gauge and an acceleration gauge.  (Navigation is easier in two dimensions as all airplane pilots are aware.)  Ahead lies a right-angle turn to the right.  The turn is along a circle.  Then the road is again straight.  Imagine what the velocity and acceleration gauge will show as you approach the turn, as you go through the turn, and as you head off in the straight line after the turn.  When you have a good feeling that you have it just right, go to the gauges.

TO THE GAUGES