Balls in circle

g = 0.1; k = 0; TMax = 500; num = 10; vxs = Table[vx, {-0.8,0.8,1.6/num}]; r = 10; tail = TMax;
f[x_, y_] := Sqrt@(x^2 + y^2);
path[vx_] := NDSolve[{x'[0] == vx, y'[0] == Sqrt[1 - vx^2],
    x''[t] ==
     If[f[x[t], y[t]] > r, -f[x[t], y[t]], 0] x[t]/
       Sqrt[x[t]^2 + y[t]^2] - k x'[t],
    y''[t] == -g - k y'[t] +
      If[f[x[t], y[t]] > r, -f[x[t], y[t]], 0] y[t]/
       Sqrt[x[t]^2 + y[t]^2]

    , x[0] == 0, y[0] == 0.1}, {x[t], y[t]}, {t, 0, TMax}];


paths = Table[path[v], {v, vxs}];
frame[T_] :=
  Show[Table[
    ParametricPlot[
     First[{x[t], y[t]} /. paths[[i]]] /. {t -> tt}, {tt,
      Max[0, T - tail], T}, PlotRange -> {1.1 {-r, r}, 1.1 {-r, r}},
     Axes -> None,
     PlotStyle ->
      Directive[Opacity[0.8],
       ColorData["RedBlueTones"][i/Length[paths]]]]
    , {i, Length@paths}],
   ContourPlot[f[x, y] == r, {x, -1.1 r, 1.1 r}, {y, -1.1 r, 1.1 r}],
   Graphics[{
     PointSize[Medium], RGBColor[0.3, 0.4, 0.9],
     Table[{Darker@Darker@ColorData["RedBlueTones"][i/Length[paths]],
       Point[First[{x[t], y[t]} /. paths[[i]] /. {t -> T}]]}
      , {i, Length@paths}]

     }
    ]
   ];
Manipulate[frame[T],{T,0.01,TMax}]