Tau[l_, g_] := Sqrt[(2*l)/(3*g)]
g = 9.81;
Remove[lösung ]
lösung[Phi0_, v0_, l_, dt_] := 
 Module[{Phi = Phi0, v = v0, a, t0 = 0, q = 0, test = {{0, Phi0}}},
  While[And [Phi <= Pi/2, q < 10000],
   {t0 += dt,
    a = Sin[Phi]/Tau[l, g]^2,
    v += dt*a,
    Phi += dt*v,
    test = Join[test, {{t0, Phi}}],
    q += 1
    }];
  test]
falltime[Phi0_, v0_, l_, dt_] := lösung[Phi0, v0, l, dt][[-1]][[1]]