Development of cocoon length over the course of evolution for the five simulation cases considered in this work. The shaded region represents the theoretically allowed zones in the length-age diagram for the extended parameter space considered across the simulations. A diverse set of behavior compared to theoretical predictions has been observed here, as discussed in Sect. 3.2.2. Notably, the blue dashed line represents the case where the jet grows at the outskirts of the ambient medium, thereby, propagating faster than the theoretical predictions.