  We investigate the time evolution of the momentum of an impurity atom
injected into a degenerate Tonks-Girardeau gas. We establish that given an
initial momentum $p_0$ the impurity relaxes to a steady state with a
non-vanishing momentum $p_\infty.$ The nature of the steady state is found to
depend drastically on whether the masses of the impurity and the host are equal
or not. This is due to multiple coherent scattering processes leading to a
resonant interaction between the impurity and the host in the case of equal
masses. The dependence of $p_\infty$ on $p_0$ remains non-trivial even in the
limit of vanishing interaction between the impurity and host particles. In this
limit $p_\infty(p_0)$ is found explicitly.
