As the arm of the trebuchet swings up due to the counterweight swinging down, the sling separates, releasing the balloon and launching it. When the balloon is first released from the shot pocket, it has an applied force moving the balloon forward and a gravitational force moving the balloon downwards. The balloon has an arcing path, of which it reaches the maximum fairly quickly in its flight. As the balloon travels, the applied force drives it (mostly) in the horizontal direction, while the gravitational force pulls it down in the horizontal direction. During its flight, the balloon encounters wind resistance (or air resistance) which slows the balloon down and makes its horizontal distance covered shorter. In order to increase range, one could arrange so that the balloon launches at a 45ยบ angle. This would give the balloon the greatest distance to travel horizontally. Also, if the launch was done in the absence of air, the balloon would travel farther.
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