Estimating Muzzle Velocity from Hang-Time Including Air Friction

grille

I made a cannon for physics in school, and now I'm having problems proving its actual muzzle velocity mathematically, from hang-time. Generally people calculate muzzle velocity neglecting friction (v=1/2gt), as if there was no big deal - when there really is huge difference.

The speeds are relatively fast, so we use this formula:All the teachers at my school (swe: "Gymnasium") just scratched their head over this, so I'm turning to this forum.



//Thanks

P.S. We shoot golf balls and here are some values to kick around:
k=0.28
m=45g
hangtime=15sec
v(term)=40m/s

P.P.S. Here is somebody doing something similar: (hxxp://www).dean.usma.edu/math/pubs/mmm99/C6.HTM

P.P.P.S. Sorry for messy post.