  In this article we revisit the projectile motion assuming a retarding force
proportional to the velocity, $\vec{F_r} = -mk\vec{V}$. We obtain an analytical
expression for the set of maxima of the trajectories, in Cartesian coordinates,
without using the Lambert $W$ function. Also, we investigate the effect of the
parameter $k$ on the radial distance of the projectile showing that the radial
distance oscillates from a certain critical launch angle and find an
approximate expression for it. In our analysis, we consider the impact of the
parameter $k$ in the kinetic energy, the potential energy, the total energy and
the rate of energy loss, and in the phase space. Our results can be included in
an intermediate-level classical mechanics course.
