Your explanation is excellent and I’m sure that most laymen interested in physics will understand it.

There are only two minor points that I would question the validity of.
One is your statement: “It is the task of physics to find out how, not why.”
The second is your statement: “Momentum is a mathematical property,.”

The second point first: From my perspective, the word “momentum” is referring to a physical phenomenon that can be expressed as a quantity, by using mathematics.

My objection to the first point is a little more involved.
To try and illustrate my perspective I will first point to Archimedes discovery of buoyancy.
Some information was obtained from the following site:

http://www.answers.com/topic/buoyancy?cat=technology

A native of Syracuse, a Greek colony in Sicily, Archimedes was related to one of that city's kings, Hiero II (308?-216 B.C.). After studying in Alexandria, Egypt, he returned to his hometown, where he spent the remainder of his life. At some point, the royal court hired (or compelled) him to set about determining the weight of the gold in the king's crown. Archimedes was in his bath pondering this challenge when suddenly it occurred to him that the buoyant force of a submerged object is equal to the weight of the fluid displaced by it.
He was so excited, the legend goes, that he jumped out of his bath and ran naked through the streets of Syracuse shouting "Eureka!" (I have found it). Archimedes had recognized a principle of enormous value—as will be shown—to shipbuilders in his time, and indeed to shipbuilders of the present.

Now the question is; did Archimedes discover only the mathematics of “how” to determine the amount of gold in the crown, or did he discover the reason “why” it was possible to calculate the amount of gold in the crown.

I believe that he “found” the reason “why” and that made it possible to calculate how much gold there was in the object.

In other words, the questions of “how” and “why” are important and should be included in scientific investigations