It was purely theoretical, and not to dispute, but your statement is incorrect. Nobody knows if tachyons do in fact exist, and until a credible theory can be raised, faster then light travel or communication cannot be disproved.
When an object breaks the sound barrier, sounds "lag" behind that object as it travels faster, theoretically the same can be said for light. Would this work the same for time? If you exceeded whatever limit this barrier has would time "lag" behind you?
A node is a location. For example, if you were planning a trip, you would of course establish a path that would get you to your destination fastest. On a map, each city would represent a node that you may travel into and away from.
Neglecting torque, the scaffold's center of mass will be proportionaly distanced in accordance to the tension on each string. This is a rather hairy calculation, so I would advise the use of Doc Al's method if you are familiar with how to calculate torque.
They will have the same PE in perspective to the point from where they were let roll. Because:
PE = {mgy}
And therefor, using the top of the ramp as your 0 height. Since Potentical Energy is perspectively based, it will be the same.
They don't occur when F(x) tends to infinity, that is the limit as x approaches positive infinity and as a way to find the Horizontal asymptote. You need to specify the use of only the highest degree terms in the numerator and denominator.
There is an easier method to finding these. It covers basically what was said above but uses more conventional methods.
Vertical Asymptote(s): X values that make the denominator zero.
Just reverse factor the zero's and you will end with the original equation. Although be careful, with...
Energy is not lost in motion. That is a dissipative force. Energy is never lost, it is transformed into another form. Such as heat, wind resistance, etc.
Just a little extra note, finding ionized atoms is not very common. Because of octet rule and how it affects the atom. So it is rare to find them in nature.