The first formula in that article boils down to a re-arrangement of:
F = mA
--> A = F/m
with velocity and acceleration written in vector form.
Knowing Drag = 0.5*(density)*Cd*(velocity)^2, we can assume that his friction constant:
C = 0.5*(density)*Cd / (mass).
It's been too many years since I've had to solve a differential equation by hand to reproduce the results without consulting my textbooks, but this exact problem and the full analytical solution was the first example given when I studied DiffEQ towards my BSAE. Most definitely not unsolved.
This same problem, when altitude-based density and gravity are incorporated, becomes much more challenging. Replace cartesian X,Y coordinates with polar coordinates planar with the trajectory around a spherical body, and x'^2 + y'^2 is no longer equal to v^2. Add also the reality that while it can generally be said that
Drag = 0.5*(density)*Cd*(velocity)^2
and Cd tends to be constant for a wide range at moderate Reynold's numbers, it varies greatly at low Rn and approaching/exceeding the local speed of sound.
Finally, it is of great importance to note that the real atmosphere , unlike the 'standard atmosphere', is not a fixed, known quantity.
For all these reasons and I'm sure some that I've forgotten, numerical solutions with lookup tables are typically far more useful in reality than purely analytical solutions.
I suspect there may have been more to the original problem than what's listed in the Reddit link. That a 16-year-old high school student figured it out on his own 'out of curiosity' is none the less very impressive.
