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I wrote a working code that plots what I need using DSolve and parametric plot. Here's an example of what it plots (and code is at the bottom).

Parametric

However, I want to be able to plot multiple graphs on the same plot with k = 0, 0.01, 0.05... Something like this Intended

I'm not sure where to vary the code without changing it too much so I can do this.

Original Code

(* Constants *)
g = 9.8;

(* Differential Equation *)
xcomp := x''[t] == -k x'[t];
ycomp := y''[t] == -k y'[t] - g;
diff := {xcomp, ycomp}

(* Initial Conditions *)
v0 = 600; \[Theta] = 60 Degree; k = 0.05;
initcond = {x[0] == 0, x'[0] == v0 Cos[\[Theta]], y[0] == 0, 
  y'[0] == v0 Sin[\[Theta]]}

(* Solve *)
eqn := Append[diff, initcond];
s = DSolve[eqn, {x[t], y[t]}, t] // Simplify
y[t_] = y[t] /. s[[1]]

(* Time of Flight *)
tof = Solve[y[t] == 0, t]; // Quiet
T = t /. tof[[2]]

(* Plot *)
ParametricPlot[{x[t], y[t]} /. s, {t, 0, T}, PlotRange -> All]
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1 Answer 1

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Here is a quick and dirty adaptation of your code for different k values:

(* different k values *)
ks = {0.001, 0.025, 0.05, 0.075};
(* constants*)
sol = (
     Clear["Global`*"]; 
      k = #;
      g = 9.8;
      (*Differential Equation*)
      xcomp := x''[t] == -k x'[t];
      ycomp := y''[t] == -k y'[t] - g;
      diff := {xcomp, ycomp};
      
      (*Initial Conditions*)
      v0 = 600; \[Theta] = 60 Degree;
      initcond = {x[0] == 0, x'[0] == v0 Cos[\[Theta]], y[0] == 0, 
        y'[0] == v0 Sin[\[Theta]]};
      
      (*Solve*)
      eqn := Append[diff, initcond];
      s = DSolve[eqn, {x[t], y[t]}, t] // Simplify;
      x[t_] = x[t] /. s[[1]]; 
      y[t_] = y[t] /. s[[1]];
      
      (*Time of Flight*)
      tof = Solve[y[t] == 0, t]; // Quiet;
     T = t /. tof[[2]];
     
     {x[t], y[t], T, k}
     
     ) & /@ ks;

Show[ParametricPlot[{#[[1]], #[[2]]} /. s, {t, 0, #[[3]]}, 
    PlotRange -> All, PlotLabels -> Placed[#[[4]], Above]] & /@ sol]

enter image description here

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