  We investigate the crossing of an energy barrier by a self-propelled particle
described by a Rayleigh friction term. We reveal the existence of a sharp
transition in the external force field whereby the amplitude dramatically
increases. This corresponds to a saddle point transition in the velocity flow
phase space, as would be expected for any type of repulsive force field. We use
this approach to rationalize the results obtained by Eddi \emph{et al.}
[\emph{Phys. Rev. Lett.} \textbf{102}, 240401 (2009)] who studied the
interaction between a drop propelled by its accompanying wave field and a
submarine obstacle. This wave particle entity can overcome potential barrier,
suggesting the existence of a "macroscopic tunneling effect". We show that the
effect of self-propulsion is sufficiently strong to generate crossing of the
high energy barrier. By assuming a random distribution of initial angles, we
define a probability distribution to cross the potential barrier that matches
with the data of Eddi \emph{et al.}. This probability is similar to the one
encountered in statistical physics for Hamiltonian systems \textit{i.e.} a
Boltzmann exponential law.
