How to calculate the actual distance flown by a golf ball? I am interested in finding out what the actual distance is flown by a golf ball on a drive.  You can assume no wind, 10 degree launch angle, goes straight down the middle of the fairway (no draw, no slice...) and no erratic backspin on the ball (so it wont "balloon" but will have stable flight).  You can also assume that the ball flies 200 yards of linear distance (relative to the ground).  So basically I would like to know how much "extra" distance does the ball fly relative to the 200 yards of linear distance?  I was thinking somewhere on the order of 15% more (30 yards more) but that is just a guess.
The answer need not be exact.
Also I am not sure what tag I should use so if someone has a better one go ahead and change it or just tell me and I will change it.

To expand the above calculations to describe a real golf ball trajectory, we need to include the effects of drag and lift (the Magnus force), when the equations become:
$\frac{\mathrm{d}\mathbf{v}}{\mathrm{d}t}= - k_D|\mathbf{v}|\mathbf{v} +
        k_L\, |\mathbf{v}|(\boldsymbol{\hat \omega}\times \mathbf{v})+ \mathbf{g}, \quad (\text{m/s}^2)$
where $\mathbf{v}(x,y,z)$ is the velocity vector, $\hat \omega$ the unit angular velocity vector, $\mathbf{g}$ gravitational acceleration vector, $t \ge t_0$ time, and $k_D$ and $k_L$ are coefficients for drag and lift forces respectively. These coefficients in turn are dependent upon the balls's spin-rate $S(t)$ and are usually defined empirically by suitable correlations.
It is the lift resulting from golf ball back-spin and surface dimples that largely contributes to the extra distance travelled, over and above that which would be achieved without this effect.
Finally, ambient conditions have to be taken into account, e.g. wind speed, air density, etc.
A fully expanded mathematical and physical description can be found in:
Griffiths (2016), Numerical Methods Using R, Cambridge University Press., Chap 9.
The full computer code (in open source language R) to perform various simulations can be downloaded from www.pdecomp.net
