fy = -9.81+if (t<0.5,T,0)

where T is 23.4 N.
what the model suggests is the thrust is 23.4 acting for 0.5 seconds at beginning of the video.

assumption

mass is constant
thrust is constant at 23.4N

my observation

the flight path is roughly close the real motion.

conclusion

of course, the model is flawed, but that is the nature of science, a better model gets made by building on other people's idea.