Object bouncing on a floor

This will make your layer/object bounce along an imaginary 'floor'. Paste it into the 'position' attribute for your layer.

After Effects 6
Design/Objects
Expressions

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Vy0 = 500; //initial y velocity (pixels/second)
Vx0 = 100; // initial x velocity (pixels/second)
g = 2500; // gravity (pixels/second/second)
floor = 400;
e = .85; //elasticity
b = floor - position[1];
h = b + Vy0*Vy0/(2*g);
T = Vy0/g + Math.sqrt(2*h/g);
if ((time-inPoint) < T){
 y = Vy0*(time-inPoint) - g*(time-inPoint)*(time-inPoint)/2 + b;
}else{
 Vy = -(Vy0 - g*T);
 while (true){
   Vy *= e;
   t = T;
   T += 2*Vy/g;
   if ((time-inPoint) < T){
     t = (time-inPoint) - t;
     y = Vy*t - g*t*t/2;
     break;
   }else if (T - t < thisComp.frameDuration){
     y = 0;
     break;
   }
 }
}
[position[0] + Vx0*(time-inPoint), floor - y]

(Min. Version: After Effects 6, Category: Design/Objects, Type: Expressions)