Physics like a mouse foraging

Grid cells and physics reasoning. In the room of classical mechanics there are objects a rectangle with mass then velocity then momentum then p=mv, another with kinetic energy, mass, velocity, E=0.5m*v^2, and so on. To solve a problem we must create a bridge from given to desired quantity.

How high does a ball thrown upward at velocity V goes?

energy is conserved
initial energy 0.5mv^2
energy at top mgh
mgh=0.5mv^2
using bridges in the math algebra room
h=(0.5*v^2)/g

It is not reasoning, it is more like playing dominoes. Simple find, move and match.