Here are a few approaches which will give you some solid answers. I don't have access to any pretty math programs, so I've not solved your example problem. You'll be making some assumptions, such as pellet shape, air temperature / density, and terrain. I'll leave it up to you to choose which approach to take, but you can solve it.
You may have tried this, but then found that it does not work well, and that it's hard. Newtownian Mechanics will give you only a rough estimation anyways.
If you are dead set on using Newtownian Mechanics, I would use some discrete math. Discrete math is good for this situation, because variables change so much. Basically, instead of figuring out the answer over long distances and times, you figure out the math for a really small distance and time, and repeat that calculation until you've covered your long distance or time. You can do this because, on smaller scales, many forces can be approximated to be constant.
I would calculate how far it travels over a small amount of time, considering the force of drag and gravity constant over that time. If I add up each of these steps, I can figure out approximately where it would go.
My algorithm would look like this:
Choose a time-step (such as .001s), define the current position (s = 0), a current speed (v = 1500), and whatever else I need (such as air density):
- Figure out the projectile's velocity at current time/position step
- Figure out current force of drag on the projectile
- Figure out the new position of the projectile given current velocity (s = v * dt)
- Go to the new position, figure out new speed given the force of drag using the speed at the previous point and the time step (v2 = v1 - F*dt)
- Repeat Until v=0, or some other interesting point in time (such as s = 50m)
That should be easy to code in most programming languages, and it should give you a decent approximation if you choose a small enough time-step. Even better, if you ever do get solid information from manufacturers, you can come back to this program and have your answers! You can also have the program print out a table of positions and times in each of these steps, so you don't have to run it a lot.
Alternatively, using Newtownian Mechanics, you could try to come up with some integrals and hope you can integrate it. However, if you're going to go through that much effort, then you may as well use Lagrangian Mechanics.
This is something that Lagrangian Mechanics solves really well. If you're comfortable with calculus, please use this over Newtownian Mechanics. I also suggest using Mathematica or similar software to help with the mathematical leg-work.
To be clear, Langrangian Mechanics works by looking at the forces involved in a system, even if they're not constant, and then figures out how the system should evolve over time given those forces. It's much more math-heavy, but it gives you very accurate results. (As a matter of fact, we've been using Lagrangian Mechanics for ballistics systems for a while now!)
In this particular case, you have the force of gravity on your object, and you have the force of air drag. Also, the angle at which you shoot will matter as well, so make sure your velocities reflects this as you express your forces.
I hope these approaches work for you!