Hey so incase anyone was wondering. The solution to my problem is called a swinging atwood machine. Mine would just be different in the fact that I would be using a force applied to the counter weight instead of gravity.
Thanks for your input! I'll refresh on my dif-eq as well! The main thing I just want to be able to figure out is at what angle should I put the tension on the line to minimize the accelerative forces on the person yet maximize their horizontal distance. I think experimental testing would be...
Imagine a standard pendulum. I understand how to work the physics on one but what if you attached that pendulum to a pulley at the top and could apply tension through the line? Let's say you released it at 45 degrees then some degrees later you applied some amount of tension through the pulley...