Let me guess that in 100 out of 100 people, the different paths of a body have immediately sprung to mind;- not formulae. And there was no consideration whatever to body size, travel limits, velocities or energy.
This is because the mind does not actually think in even english words, never mind formulae. It thinks in pictures of blocks of mechanical things working in spatial and dynamic relationships;- that the words and formulae evoke.
We merely EXPRESS our thoughts in common word and math symbols in order to communicate. But if that fails, we invariably fall back on pictorial illustrations, as real-to-life as we can make them. This is why people use easy-to-understand analogies, parables, metaphors, similies and allegorical language in order to get a difficult mentally-generated intangible concept across.
This is why engineers make rough sketches first, then do feasability math, then do scaled pictorial drawings and then add dimension values in print. With typical CAD programs, many of the drawing components are even assigned specific colors. Then the electrical is differently colored from plumbing.
In the case of waves, for instance, Michelson and Morley used a boat-on-a-water-stream. And THEN they put the math to it. Unfortunately, because they did not understand the mechanical nature of waves, and erroneously thought them identical to a boat, they used an analogy that did not fit.
So these things happen. But the basic idea of using analogies is very legitimate. However, no analogy is perfect, or it would be the thing represented.
In which case, math must be used with extreme caution. One cannot say that because boats and waves are both lumps of stuff, all the attributes of one can be transferred to the other. M&M tried to make boats out of waves, but it is absurd to try to say that we can use wave mechanics and wave math to describe a boat. Then the converse is also absurd.
The Rules for Waves and Bodies-of-Matter-in-Flight, are Different (I say).
The attributes of light waves cannot be assigned to particles of matter.
And the compression / extension of the wavelength of water-waves cannot be transferred to boats.
In like manner, the c/e of light-waves cannot be transferred to length-of-matter-body and time.