v=2;g=1;ω=Pi/300;r=0.2;h=21;
z[t_]:=h-2.5 n[t] + 1/16 v (t-75 n[t]) - 1/2 g (1/16(t-75 n[t]))^2;
n[t_]:=Which[t≥0&& t< 75,0,t≥ 75&&t< 150,1,t≥ 150 && t<225,2,t≥225&& t< 300,3,t≥ 300&&t< 375,4,t≥375&& t< 450,5,t≥ 450&&t< 525,6,t≥525&& t< 600,7];Animate[Graphics3D[{{Sphere[{2Cos[ω t],2Sin[ω t],z[t]},0.5]},{Cylinder[{{2Cos[0],2Sin[0],0},{2Cos[0],2Sin[0],h}},r]},{Cylinder[{{2Cos[Pi/4],2Sin[Pi/4],0},{2Cos[Pi/4],2Sin[Pi/4],h-2.5}},r]},
{Cylinder[{{2Cos[Pi/2],2Sin[Pi/2],0},{2Cos[Pi/2],2Sin[Pi/2],h-5}},r]},{Cylinder[{{2Cos[3Pi/4],2Sin[3Pi/4],0},{2Cos[3Pi/4],2Sin[3Pi/4],h-7.5}},r]},
{Cylinder[{{2Cos[5Pi],2Sin[5Pi],0},{2Cos[5Pi],2Sin[5Pi],h-10}},r]},{Cylinder[{{2Cos[5Pi/4],2Sin[5Pi/4],0},{2Cos[5Pi/4],2Sin[5Pi/4],h-12.5}},r]},
{Cylinder[{{2Cos[3Pi/2],2Sin[3Pi/2],0},{2Cos[3Pi/2],2Sin[3Pi/2],h-15}},r]},{Cylinder[{{2Cos[7Pi/4],2Sin[7Pi/4],0},{2Cos[7Pi/4],2Sin[7Pi/4],h-17.5}},r]}},Lighting->Automatic,PlotRange->{{-3,3},{-3,3},{0,25}}],{t,0,600,1}]