  Dynamics near the grazing manifold and basins of attraction for a motion of a
material point in a gravitational field, colliding with a moving
motion-limiting stop, are investigated. The Poincare map, describing evolution
from an impact to the next impact, is derived. Periodic points are found and
their stability is determined. The grazing manifold is computed and dynamics is
approximated in its vicinity. It is shown that on the grazing manifold there
are trapping as well as forbidden regions. Finally, basins of attraction are
studied.
