Why doesn't velocity enter into Heisenberg's Uncertainty Principle? So I came across Heisenberg's uncertainty principle in my 11th grade book, and I'm not convinced. It says $\Delta x \Delta p \gt \frac{h}{4\pi}$. Okay, but how does velocity even matter to determine the path?

Now suppose we have, for the case of my argument, 100 exactly identical atoms of hydrogen. Now we find the positions of the lone electron in 100 different cases, and we can do it with 100% accuracy. Now, if we join the dots, won't we get the path of the electron? Why not? Please explain in simple words if you can.
Some problems with your method: you mention taking 100 copies of the same atom of hydrogen and finding the positions at 100 different times. (i) You actually can't make a copy of a quantum system without knowing its quantum state (the no-cloning theorem), (ii) your measurements of position will disturb the "trajectory" of the electron, so your 100 cases are distinct and cannot represent the path of a single electron, and this is especially true the more accurate you make your measurements.

You should realize, however, that the bound placed by the Heisenberg uncertainty principle is really quite small, and on a macroscopic scale we can essentially determine the trajectory of an electron. A bubble chamber or cloud chamber is essentially a major revision of your proposed method: we fill a vessel with supersaturated vapor, wait for charged ions to pass through the vapor and cause it to condense, and observe the resulting tracks. This describes the ion's motion with a resolution on the order of microns.