Build a Catapult or Trebuchet from cardboard.
Specifications:
Comparison of balls:
Potential energy of counterweight:
Kinetic energy transfered 100% results in velocity
https://www.omnicalculator.com/physics/range-projectile-motion
https://www.amesweb.info/Physics/Projectile-Motion-Calculator.aspx
Values:
Realistically we can probably transfer only 50% of the potential energy to the kinetic energy. This leaves us with 0.069 Joule and a resulting velocity of 7.1 m/s. Using the distance calculator and a height of only 30 centimeters (the axle) the maximum distance is 5.47 meter.
You want to calculate the maximum distance by yourself? That's great! I created a Jupyter notebook where you can play around with the values and see how it works. Here is the pdf version. The central point is the formula for the distance: