The fourth dimension is technically time. the fourth dimension that you are talking about is actually impossible to comprehend.
The tree might get swept away by the current and it will disappear when it catches on something
Well velocity is a vector quanity and we can brake vectors in to verticle and horizantal componontes threw these two formulas Vcostheta=Vx and Vsintheta=Vy
Answer:
Now, think on the electrons flowing through a conductor (we can think on the resistor as a simple conductor, like a piece of metal)
Inside the conductor, we have some "fixed" (they do not flow with the current) electrons, such that as the current flows in the conductor, the flowing electrons can interact with the fixed ones in the conductor. Then we can have collisions inside the conductor.
In those collisions, the flowing electrons leave energy in the conductor, and as we know, heat is a form of energy. Then when we have a lot of these collisions, the temperature of the conductor increases.
That is why electronic devices get hot.
Also, as the temperature of a conductor increases, the electrons inside of it start to move more, then the probability of an interaction with the flowing electrons increases.