  I discuss the influence of adding the air resistance and the kinetic friction
to the classical mechanics homework-problem: finding the motion of a body
sliding down a hemispherical hill. For a physically realistic ($\propto v^2$)
form of drag force thus modified problem interestingly turns out to still admit
analytical solutions of motion equations. I counter-intuitively find that even
if friction coefficients are much larger than those of drag (as compared in the
appropriate units), the drag effects remain significant. I also discuss how the
transition between two possible outcomes of the motion (flying off and halting)
is modified in the presence of the drag force coefficient with respect to the
friction-only problem. I examine the behavior of the system using both the
perturbation theory and exact analytical solutions of differential equations,
showing that one can gain interesting insights from two different but
complementary standpoints.
