  We investigate the ability of jets in active galactic nuclei (AGNs) to break
out of the ambient gas with sufficiently large advance velocities. Using
observationally estimated jet power, we analyze 28 bright elliptical galaxies
in nearby galaxy clusters. Because the gas density profiles in the innermost
regions of galaxies have not been resolved so far, we consider two extreme
cases for temperature and density profiles. We also follow two types of
evolution for the jet cocoons: being driven by the pressure inside the cocoon
(Fanaroff-Riley [FR] I type), and being driven by the jet momentum (FR II
type). Our main result is that regardless of the assumed form of density
profiles, jets with observed powers of <~ 10^{44} erg s^{-1} are not powerful
enough to evolve as FR II sources. Instead, they evolve as FR I sources and
appear to be decelerated below the buoyant velocities of the cocoons when jets
were propagating through the central dense regions of the host galaxies. This
explains the reason why FR I sources are more frequent than FR II sources in
clusters. Furthermore, we predict the sizes of X-ray cavities from the observed
jet powers and compare them with the observed ones --- they are consistent
within a factor of two if the FR I type evolution is realized. Finally, we find
that the jets with a power >~ 10^{44} erg s^{-1} are less affected by the
ambient medium, and some of them, but not all, could serve as precursors of the
FR II sources.
