[GeeTwo]

Assuming you can keep your slide from binding, whether a single motor can lift a given load is a function of power and appropriate gear ratios more than if you have a linear slide or rotating arm or cable winch or whatever. A linear slide is slightly more complicated and heavier, but gives better control. Deciding which mechanism type is optimal is a matter of balancing your strategy, requirements, and capabilities.

Calculate the weight of the load, multiply by the height, and divide by the time you are willing for that load to take to get to that height, and that's the output mechanical power you need (unit converters are available online to get oz-in/sec or whatever to Watts). Make sure your motor(s) can produce 150% or more of this power for that amount of time. If the time is really short (so that the ball is still accelerating noticeably halfway down the track), you'll need more power to account for the kinetic work.

Once you identify the motor, figure out what gear ratio converts the speed that the motor spins into the distance the ball moves.

JVN has a calculator on CD that will do all of this pretty easily at FRC scale; there may be similar calculators for FTC. If you come up with the specifics you're looking for, post your work and we'll check it for you, or post the specific loads and heights and stuff and we'll guide you through the calculations.