I don't know why you think it should be 0.
Calculate each derivative and plug the values into the formula. You should get 1. Remember that x and p are independent.
The previous suggestions are excellent. But I'm going to suggest something along a different line:
Number theory.
It's fun.
It's simple enough that you don't have to worry about it being too difficult for a high school math teacher.
There are many easy-to-state but unsolved...
Granted. Tribbles are discovered on Mars and brought back to Earth. Two weeks later, there is nothing to eat but tribbles.
Granted. You are now a genie. You are imprisoned in a little lamp that is resting at the bottom of the ocean. You can only grant wishes for other people, and you must...
I made the decision to believe quantum mechanics when I was a college sophomore taking a class in modern physics. I think the biggest factor was learning about the results of double slit experiments. But it was a gradual process similar to the one you described.
A more dramatic change...
When I was young, I did not believe relativity or quantum mechanics. Now I do. My change in belief was definitely a choice. I considered the evidence for the theories and made a decision based on that.
I've changed my beliefs about many things over the years.
This is correct except that KQ/2 should be replaced by K(Q^2)/2. Brett here is splitting the forces into vertical and horizontal components, which works just as well as using the diagonal components.
In reality, it does happen. Rocket scientists take advantage of the rotation of the Earth to give rockets extra speed. It is the reason why rocket bases are often located in tropical regions.
The outer product of two vectors is a simple tensor.
u^a v^b = w^{ab}
So for visualization purposes, you can imagine a tensor as a pair of arrows emanating from the same point.