  The accretion model for the nineteenth century Great Eruption (GE) of $\eta$
Carinae suggests that mass outflowing from the primary was accreted onto the
secondary, and the gravitational energy of that mass accounts for the increase
in luminosity and most of the kinetic energy of the ejecta. It further argues
that the accretion was accompanied by the ejection of two jets that shaped the
bipolar Homunculus nebula. Observations of echos from the GE found emission
lines with broad wings suggesting some of the mass in equatorial directions
reached more than $10\,000 \,\rm{km\,s^{-1}}$. We run hydrodynamic simulations
following periastron passage during the GE, launching jets from the secondary
as it accreted gas erupted from the primary. We then follow the interaction of
the polar jets with the surrounding primary wind, as they accelerate part of
the flow to velocities $ > 10\,000 \,\rm{km\,s^{-1}}$ and deflect it towards
lower latitudes. We find that the amount of mass that reached these high
velocities during the GE is $M_h \approx 0.02 \,\rm{M_{\odot}}$. This value
reaches maximum and then decreases with time. Our simulations agree with
previous results of the accretion model from which we estimate $M_h$ taking
into account the energy budget of the GE. The accretion model can explain the
observations of high velocity gas in light echos with the known two stars, and
a triple star system is not required.
