# Plotting multiple dependent variables with DSolve (projectile motion with air resistance)

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).

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

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] ``