Bouncing explosion

(* this code is really slow, and could be sped up by caching the number of bounces before t calculation*)
g = 0.05;
c = 0.9;
path[vx_, t_] :=

  Module[{\[Tau] = (2 Sqrt[1 - vx^2])/g, found, m, prev},
   found = False; m = 0; prev = 0; While[found == False && m < 100,
    found = Sum[(2 c ^n Sqrt[1 - (vx)^2])/g, {n, 0, m}] > t; m++;
    If[! found,
     prev = Sum[(2 c ^n Sqrt[1 - (vx)^2])/g, {n, 0, m - 1}];];];
   \[Tau] = Sum[(2 c ^n Sqrt[1 - (vx)^2])/g, {n, 0, m - 1}];
   {vx t, (c^(m - 1) Sqrt[1 - (vx) ^2] tt - 1/2 g tt^2) /. {tt ->
       t - prev}}];
xmax = 50;
anim[T_] :=
 Show[
  Table[
   ParametricPlot[path[vx, t], {t, 0, T},
    PlotRange -> {{-xmax, xmax}, {-1, 10}}, Axes -> None,
    PlotStyle -> RGBColor[0.8, 0.6, 0.3]],
   {vx, -0.9, 0.9, 1.8/40}
   ],
  Graphics[
   {Thick, RGBColor[0.6, 0.8, 0.9],
    Line[{{-xmax, 0}, {xmax, 0}}],
    Black, PointSize[Medium],
    Table[
     Point[path[vx, T]]
     ,
     {vx, -0.9, 0.9, 1.8/40}
     ]
    }]
  , ImageSize -> 300, AspectRatio -> 1];
frames = Table[Rasterize@anim[x], {x, 0.01, 100}];
Export["bounces.gif", frames];