g=9.81;m=0.5;
Fnce[ypoc_,dt_]:=(
t=0;y=ypoc;v=0;

Trajektorie={{t,y}};
While [y>0,
Fy=-g*m;
 a=Fy/m;
v=v+a*dt;
y=y+v*dt;
t=t+dt;
AppendTo[Trajektorie,{t,y}];
];
ListPlot[Trajektorie, PlotMarkers->{•,7}])

Tr1=Fnce[45,0.001]

Tr2=Fnce[125,0.001]

Tr3=Fnce[45,0.01]

Trajektorie

Tr4=Fnce[45,0.1]

Trajektorie

Tr5=Fnce[45,1]

Trajektorie

NumSol=Show[Tr1,Tr3,Tr4,Tr5, ImageSize->700]

AnSol=Plot[45-1/2 9.81 (t^2),{t,0,3},PlotStyle->{Red, Thickness[0.015]}, ImageSize->700]

Clear[y,t];
TrNDS=NDSolve[{y''[t]==-g,y'[0]==0,y[0]==45},y,{t,0,3}];
NDSol=Plot[Evaluate[y[t]/.TrNDS],{t,0,3},PlotStyle->{Green,Thickness[0.01]},ImageSize->700,PlotRange->All]

Show[AnSol, NDSol,NumSol]