RK23[f_,u0_,t0_,T_, h0_, tol_]:=(
h=h0;
t=t0;
y={0};
y[[1]]=u0;
i=1;
t={0};
While[y[[i]][[2]]≥0,
k1=h f[t[[i]],y[[i]]];
k2=h f[t[[i]]+h,y[[i]]+k1];
k3=h f[t[[i]]+(h/2),y[[i]]+(1/4)k1+(1/4)k2];
While[Norm[((1/3)(k1+k2-2k3)),Infinity]/Norm[y[[i]],Infinity]>tol,
h=h((((tol/(Norm[((1/3)(k1+k2-2k3)),Infinity]))))^(1/3));
k1=h f[t[[i]],y[[i]]];
k2=h f[t[[i]]+h,y[[i]]+k1];
k3=h f[t[[i]]+(h/2),y[[i]]+(1/4)k1+(1/4)k2];
];
y=Append[y,y[[i]]+(1/6)k1+(1/6)k2+(2/3)k3];
t=Append[t,t[[i]]+h];
h=h((((tol/(Norm[((1/3)(k1+k2-2k3)),Infinity]))))^(1/3));
i++
];
y
)

m=15; 
c=0.2;ρ=1.29;s=0.25;g=9.81;v0=50;θ0=0.6;T=0;
u0={0,0,v0,θ0};
f[t_,y_]:={y[[3]] Cos[y[[4]]],y[[3]] Sin[y[[4]]],1/m(T-1/2 c ρ s ((y[[3]])^2))-g Sin[y[[4]]],-g/y[[3]] Cos[y[[4]]]}
res=RK23[f,u0,0,10, 0.0001, (10^(-2))];
points=Table[{res[[i]][[1]],res[[i]][[2]]},{i,1,Length[res]}];
plotAppr1=ListLinePlot[points];
θ0=1.2;
u0={0,0,v0,θ0};
f[t_,y_]:={y[[3]] Cos[y[[4]]],y[[3]] Sin[y[[4]]],1/m(T-1/2 c ρ s ((y[[3]])^2))-g Sin[y[[4]]],-g/y[[3]] Cos[y[[4]]]}
res=RK23[f,u0,0,10, 0.0001, (10^(-2))];
points=Table[{res[[i]][[1]],res[[i]][[2]]},{i,1,Length[res]}];
plotAppr2=ListLinePlot[points];
Show[plotAppr1,plotAppr2,PlotRange->All]

Manipulate[Show[ListPlot[{{res[[k]][[1]],res[[k]][[2]]}},PlotMarkers->"",PlotRange->{{0,200},{0,250}}],plotAppr2],{k,1,Length[res],1}]