  In the $N$-body problem, a motion is called hyperbolic, when the mutual
distances between the bodies go to infinity with non-zero limiting velocities
as time goes to infinity. For Newtonian potential, in \cite{MV20} Maderna and
Venturelli proved that starting from any initial position there is a hyperbolic
motion with any prescribed limiting velocities at infinity.
  Recently based on a different approach, Liu, Yan and Zhou \cite{LYZ21}
generalized this result to a larger class of $N$-body problem. As the proof in
\cite{LYZ21} is quite long and technical, we give a simplified proof for
homogeneous potentials following the approach given in the latter paper.
