This post is long, I apologize. If you are interested in this topic, I believe my post is worth the time it will take to read it.
Something I haven’t seen posted on here so far: Breaking the forces up into components. For this problem, it is much easier to understand if it is broken into vertical and horizontal components. If you can get an accurate reading of its horizontal speed, this speed is constant throughout the flight.(we are neglecting air resistance) Also, if you know the height the ball reaches you can find the initial vertical speed of the ball. This vertical speed won’t be affected by the carpet because the carpet only affects the horizontal component.(directly) Now, once we have this…we can model its flight from the moment it leaves the ground to the moment it lands and the energy within the ball during this time. However, to model the actual kick…there is more to it. It really depends on how the kicker is designed, but I’m going with a leg with one joint. If you can find the speed it is rotating with, you can find the energy within the kicker upon impact. However, to do this math you must understand rotational inertia and angular speed. To explain angular speed, I’d suggest a merry go round. Explain how the linear speed changes with distance from the middle, but the angular speed is constant. As for rotational inertia, that is a bit harder. Try getting an item with high rotational inertia and an item with low rotational inertia. Put them both on a wheel or something and let them spin them. If the inertias are different enough, they will feel the difference in resistance. Ideally, they should have the same mass so they don’t mistake the mass to being the sole cause of the increase in difficulty. Other then that, I’d just use a formula to calculate the actual rotational inertia of the kicker. Now, you can use the above data to find the energy in the kicker before the kick. This allows us to see the energy before the kick. We can now use the difference of energies(the ball after the kick, and the kicker before the kick) and we will see the energy lost due to the actual kick. Some of these losses were explained above in other posts. I’d go over them briefly with the student’s but not go into too much depth on the actual math behind them.
Now, with the above explanation they get a thorough understanding of explaining what you can’t understand by using what you can. Also, it teaches them rotational inertia by experiment(something my college never really did properly and is largely the reason it took so long for people to understand it). It also teaches them angular velocity which also confuses some if you don’t get a good visual. After they understand all of this, they might be able to come up with a way to increase the distance of the ball by increasing the energy within the kicker prior to the kick. For instance, do we want a kicker with high rotational inertia? If so, how can we increase it? If not, how can we decrease it?
I know my explanation above explains alot of concepts that they don’t go into fully in high school level physics. However, they are concepts that could be grasped by their age group with proper explanation and visuals. I chose these concepts because they are the concepts college kids sometimes don’t understand, and ensures that your students will benefit greatly from the experience. If nothing else, exposing them to these ideas will have a positive effect.
If anyone has questions, feel free to PM me. Also, if some part of this is wrong(I’m pretty sure all the concepts are there) please respond immediately.
haha