Anyone who knows the topic properly? Can offer fg for help of course

Porogramme need to have a possibility of determining the:
-density and viscosity of fluid
-diameter and density of ball
-step size (h)
-number of steps (integration time)
Buit firstly have to be done for free falling ball in a vacuum. I know i have to use the Runge Kutta 4th order solution method. Started and got this at teh moment:
Falling in vacuum:
m*(dV/dt) = m*g
V = V(initial) + g * t
Z = Z(initial) + V(initial) *t + (g*t^2)/2
where g works as our acceleration. so after differentiation:
dV/dt = d^2 Z/dt^2
then i have to add forces that affacets the body during motion:
bouyant force according to Archimedes principle,
force due to body acceleration,
forces due to viscous drag and shape drag
Can send you whole materials if theres anyone who can solve that problem and write in c++ or at least gimme some thoughts, Never made anything like that and that's the problem xP