I have begun to author a number of guides, as many seem to have forgotten the physics and math required. Alas, as a rookie mentor I have had good feedback from those whom I’ve asked for review (as done Saturday/Sunday) but also warnings not to get burned out. I suppose authoring these is great a great way to study for the PE Exam. Now that May will mark 5 years since graduation with my BSME, I should begin studying. 
My “Guide” in the link below will allow you to know the exit velocity of your soccer ball from your bot given a desired distance of travel. Included are links to MATLAB code for the final charts. (Did with my work license, can we get MATLAB free as mentors or can the students?)
If you desire to figure out the input energy (how far to draw back a spring, charge a cylinder, etc…), no promises, that “white paper” should be released (will also place here) on Friday or Saturday. Any mechanical engineer or physics mentor should be able to help a student run the equations for an inelastic colission easily enough. You can do a fun experiment with the kids to find the coefficient of restitution which is simply the square root of the ratio of rebound. (height bounced to / height dropped from) Or, just wait til Friday, and all will be explained. The second one I will attempt to format more as a “lesson plan” assuming education level of Physics = minimal, Math = Pre-Algebra / Algebra 1.
The second paper will also cover (very important) the relationship between velocity and mass of your “foot”. It is logical a fast, light foot is worthless. It is also logical a foot so heavy that it is difficult to get up to speed and therefore moves slowly, is also pretty much worthless. So a middle ground exists. Can numbers describe? YES (but not give ideal, only help you to “tune” your design)
Trajectory Evaluation for Strategy Selection and Shooter Design
Best Regards, and feedback always welcome.
John J Baldauf (eaglecat)
Gear it Forward - FRC Team 2338
First Year Mentor
Engineer, Caterpillar Inc. (Lead Sponsor for 2338)