  We studied the dynamics of an object sliding down on a semi-sphere with
radius $R$. We consider the physical setup where the semi-sphere is free to
move over a flat surface. For simplicity, we assume that all surfaces are
friction-less. We analyze the values for the last contact angle $\theta^\star$,
corresponding to the angle when the object and the semi-sphere detach one of
each other. We consider all possible scenarios with different combination of
mass values: $m_A$ and $m_B$, and the initial velocity of the sliding object
$A$. We found that the last contact angle only depends on the ratio between the
masses, and it is independent of the acceleration of gravity and semi-sphere's
radius. In addition, we found that the largest possible value of $\theta^\star$
is $48.19^{\circ}$ that coincides with the case of a fixed semi-sphere. On the
opposite case, the minimum value of $\theta^\star$ is $0^\circ$ and it occurs
then the object on the semi-sphere is extremely heavy, occurring the detachment
as soon as the sliding body touches the semi-sphere. In addition, we found that
if the initial kinetic energy of the sliding object $A$ is half the value of
the potential energy with respect to the floor. The object detaches at the top
of the semi-sphere.
