  After release from the trap the momentum distribution of an impenetrable gas
asymptotically approaches that of a spinless noninteracting Fermi gas in the
initial trap. This phenomenon is called dynamical fermionization and, very
recently, has been experimentally confirmed in the case of the Lieb-Liniger
model in the Tonks-Girardeau regime. We prove analytically and confirm
numerically that following the removal of axial confinement the strongly
interacting Bose-Fermi mixture exhibits dynamical fermionization and the
asymptotical momentum distribution of each component has the same shape as its
density profile at $t=0$. Under a sudden change of the trap frequency to a new
non-zero value the dynamics of both fermionic and bosonic momentum
distributions presents characteristics which are similar to the case of single
component bosons experiencing a similar quench. Our results are derived using a
product representation for the correlation functions which, in addition to
analytical considerations, can be implemented numerically very easily with
complexity which scales polynomially in the number of particles.
