  We present a semiclassical treatment of a fermionic impurity coupled to
Bogolyubov modes of a BEC. In the lowest order approximation we find a full
solution of an initial value problem, which turns out to behave differently in
the sub- and supersonic regimes. While in the former case no impurity
deceleration is observed, in the latter case non-Markovian dissipation effects
kick in resulting in slowing down of the fermion. Although this scenario is
compatible with the one offered by an elementary field theoretical picture at
weak coupling, the details of the dynamics turn out to be completely different.
Fluctuation effects can be taken into account by expansion around the classical
path. This allows for estimation of the all-important polaron radius as a
function of fermion-boson coupling strength. As an application we calculate the
drag force which is exerted by the BEC on the impurity moving with constant
velocity $v$. Contrary to the perturbative result, according to which the drag
force is $\sim v^4$, it turns out to be proportional to $1/v^2$ in the
semiclassical regime.
