In case you missed my response before (more than one of us responded), reading that first will probably make this a little clearer...
Gravity is related to how far the ball will travel given an initial velocity. The velocity will have a component in the horizontal direction, which doesn't change (if you ignore air resistance), and a component in the vertical direction. Because gravity produces a force in the vertical direction, the ball's upward motion will be slower and slower until it stops for just a moment and begins to move downward. Eventually it hits the ground and the horizontal motion stops for that reason. This is interesting and good to understand, but I don't think it explains why your experiment didn't work. You could divide this into two stages:
(a) Why the experiment should work for a kicked ball:
What you're interested in is what determines the ball's initial velocity right after you kick or otherwise propel it. If the kick is the same every time, then this has to do with the elasticity of the collision. Some good search terms would be physics collision
or inelastic elastic collision
, and here are some good results to get you started:http://en.wikipedia.org/wiki/Collisionhttp://www.walter-fendt.de/ph14e/collision.htmhttp://hyperphysics.phy-astr.gsu.edu/Hbase/elacol.html
Then you have to think about what determines the elasticity of a ball (and therefore the elasticity of its collision with a foot), and this is where the pressure comes in. This is a really neat bounce simulation where you can change the pressure inside the ball, and it shows an animation with the compression and "efficiency", which is related to the elasticity of the bounce:http://www.xmas.demon.co.uk/bouncyBall/bouncy.html
This is a paper explaining where the equations used in the simulation come from -- it's pretty technical, so please do ask specific questions about it if you feel up to tackling it:http://www.iop.org/EJ/article/0031-9120 ... 8120fa091b
There's a chapter on bouncing in this book, some of which is available online -- sorry that it's the wrong sport. http://books.google.com/books?id=ZZizYIQcZ60C
If you aren't familiar with the ideal gas law, it might also give you some insight:http://en.wikipedia.org/wiki/Ideal_gas_law
For your purposes, you can probably assume that nRT is constant (that's just the number of air molecules, the temperature, and a constant to make the units work out). When the ball deforms, the volume changes, so the pressure inside the ball has to change. If the volume is divided by two, then the pressure doubles, and so on. So, when the ball deforms, the volume decreases and the pressure inside actually increases, and this is the force that makes the ball move -- otherwise it would just sit there with a dent in it.
(b) Why it didn't work in your case with the catapult:
Without actually seeing a picture of your catapult, I would guess that there are two differences between it and kicking. One is that the force is probably applied over a larger area, so there is less pressure on any given part of the ball's surface. The other is that the catapult probably "carries" the ball through a certain distance to get it up to speed. That means that less force is being applied but for a longer period of time compared to a kicked ball that ends up going to same speed. Think about it this way: Imagine you're standing still wearing roller skates, and a friend pushes you gently from behind until finally your friend is running and you're just in front going the same speed. Now imagine that instead, you're standing still and your friend runs up from behind, pushing all at once to make you go the same speed you ended up going before -- that would probably hurt both of you. A bone in your friend's hand could deform
enough to break, or cells in your skin could deform enough to leak blood, resulting in a bruise. You could also think about baseball: The pitcher swings the ball through a long arc to get it up to speed and it doesn't hurt his or her hand, but no one wants to be hit by that ball or to catch it without a glove. In the same way, the ball might not deform much when accelerated over a distance with the catapult, but it would deform pretty easily when kicked quickly.
I think that if you work hard to understand why the experiment should work with a kicked ball, that should answer your questions about why it didn't work with the catapult and what you could do differently. It's awesome that you're persevering with this even though it's gotten complicated!