To bounce or not to bounce?

In EOE, Master Su has chosen 3 principles (that I know of) to explain important ways to strike. He starts by bouncing a ball off the floor. He later shows a sandbag being dropped and "sticking" to the floor. Lastly, I have been told that the next evolution of these two principles is that of a glass bottle being dropped and shattering. What do these three scenarios demonstrate? What physical properties do these three impacts show us?

I am not sure what Master Su had in mind when choosing these 3 principles, but I can tell you what I know from physics about these three cases. These cases seem to denote corner cases to the types of collisions possible. In a collision, maximum momentum transfer occurs from a projectile to it's target in a perfectly elastic collision. Conversely , maximum inelasticity allows for maximum energy dissipation in collisions.

Maximizing Momentum Transfer

Momentum must be conserved in a closed system. This means that the total momentum before and after a collision must be equal in this system. Momentum is simply the product of an object's mass and its velocity (P = mv, P is used to denote momentum). The total momentum between two objects is the sum of their individual momentums. It is important to note that momentum is a vector, not a scalar, it has direction!

What happens to momentum during a collision? Well simply speaking, if one object slows down (looses momentum), another object must pick it up (gain momentum). So the more a projectile slows down, the more momentum is transfered to its target. At first thought one would think that if the projectile comes to a complete stop, it has transferred all of its momentum so this must be the greatest possible momentum transferral. This is true, when a projectile and its target have the same mass. But if the projectile is less massive, an even greater momentum transfer can be achieved by a bounce. In a perfectly elastic collision, the smaller the mass of the projectile compared to the target, the more the projectile will bounce.

If we want our target to be maximally accelerated, we should create a maximally elastic collision, like a ball bouncing off the floor.

Maximizing Energy Dissipation

If the projectile and the target are of equal mass, then the maximum energy is dissipated in the collision if they stick together and move at equal speeds after the collision. This creates the lowest velocities for both objects which results in the least amount of kinetic energy.

Question

Throw a rubber ball at a can and throw a sandbag of equal mass to the ball at the same can, which one will project the can furthest?

Missiles

The above scenarios described simple collisions, collisions free of energy inputs. Now imagine a thrust based missile, or a human running. It is possible to continue to input energy into a collision throughout and even after the collision.

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Notes on training

It is a good idea to start to learn how to strike by hitting a horizontal pad (on a table or other flat surface) with your palm. Since striking down is fairly intuitive, this should be easy, but with some simple attention to your motion you can immediately improve your striking speed and power.

Try the following steps in order. Some step may seem trivial, but they are well worth the time you spend understanding them and making them repeatable. The steps are:

Bouncing

First try to make your palm hit and immediately bounce back to the height it came from. This should become easy. Bounce repeatedly and cleanly several times in a row. You should not have to "lift" your hand after the strike. Throw your hand at the pad and it should easily rise after hitting. You are developping a nice "wavelike" motion in your arm and wrist. Do not neglect this step. It is a model for all your motions since to do this right you must move naturally with little tension.

Extend Your Range

Next, extend the range of your strike. Start your strike higher and higher. Then try lowering your striking surface, lower it to maybe the level of a bench. In order to hit it that low you will have to start using your legs and your body, this will get you ready for the next step. Do not stay squatting to hit the pad over and over, always come all the way back up afterward. This will force you to use your whole body when hitting.

Stick

Lastly, we want to stick to the pad. Bring the pad back to normal (table) height, and strike it a few times bouncing followed by sticking to it on the third strike.