Let's start with
fd[v_] :=-αd*Abs[v]^2*Normalize[v]
fl[v_] := αl*Abs[v]^2*l
fl[v_] := -m*g*{0, 1}
f[t_] := fd[v]+fd[v]+fd[v]
Do you perhaps mean something more like
fd[v_] :=-αd*Abs[v]^2*Normalize[v]
fl[v_] := αl*Abs[v]^2*l
fg[v_] := -m*g*{0, 1}
f[t_] := fd[v]+fl[v]+fg[v]
But that definition of f[t] doesn't seem right either. Maybe you mean
f[v_]:=fd[v]+fl[v]+fg[v]
but I'm not sure that is right either.
Next let's look at a[t]
In[20]:= a[t_] := f[t]/m
a[t]
Out[20]= {0., -9.81}
and that value is unchanged if I try a[0] or a[5] or a[1000].
Next let's look at what you are going to give to DSolve
In[21]:= {D[r, {t, 2}] == a[t], x[0] == 0, y[0] == 0, v[0] == 60}
Out[21]= {0 == {0., -9.81}, x[0] == 0, y[0] == 0, 0[0] == 60}
That doesn't look like a differential equation.
Can you use this to try to fix some problems before you try to give it to DSolve?