g=9.8; γ=1/36.6;
v0=40;
T0=(v0/g)
Hmax=((v0^2)/(2g));
Ttop=(1/(γ g))ArcTan[γ v0]
Tend = (1/(γ g))ArcCosh[(Sqrt[1+(((γ v0))^2)])]
sol1=NDSolve[{z'[t]==(1/γ)Tan[-γ g t+ArcTan[γ v0]],z[0]==0},z[t],{t,0,2}];
zdn[t_]=(1/((γ^2)g))Log[((Sqrt[1+(((γ v0))^2)])/(Cosh[γ g t]))];
g0=Plot[v0 t-(1/2)g (t^2),{t,0,2T0},PlotStyle->Cyan];
g1=Plot[Evaluate[z[t]/.sol1],{t,0,Ttop},PlotRange->{{0,2T0},{0,Hmax}}, PlotStyle->Red];
g2=Plot[zdn[t-Ttop],{t, Ttop, Ttop+Tend},PlotStyle->Blue];
Show@{g0,g1,g2}