Since you were all so concerned about my Physics teacher, he happens to be my roommate and the one that created the sim pole drop program. I'll let him handle this issue
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He is an aerospace engineer at UCLA, this might get technical
Okay, there's some confusion here in regards to reference frames. In the situation we're working with, I'm assuming that the pole vaulters are running as fast as they can. If this is the case then there is an initial burst of acceleration to reach their top speed. After reaching their top speed they will no longer be accelerating because, well, they've reached their top speed. If anything they might slow down. Regardless, once they've reach their top speed any speed changes afterwards are most likely negligible. Also worth noting is that their top speed is reached well before the pole has started dropping (at least in the technique we're working with).
What this all boils down to is that when analyzing the pole fall we can safely make the assumption that the pole vaulter is moving at a constant velocity. When dealing with the pole fall we take a reference frame relative to the runner. If the runner is moving at a constant velocity then this reference frame is an inertial reference frame so there are no external forces acting on the pole (other than gravity). In other words, we can treat the pole fall as if it was just falling from rest.
The situation you guys describe is with an accelerated reference frame (the pole vaulter speeding up). If the pole vaulter was accelerating while dropping the pole then the pole will indeed fall slower or even fall behind the pole vaulter. However, this only occurs with an accelerated reference frame (i.e. when the pole vaulter is speeding up). That acceleration amounts to a force forward at where the pole vaulter is holding the pole. This is thanks to Newton's Second Law, F=ma. The force is a function of acceleration so if the pole vaulter is speeding up then he/she generates an acceleration that results in a force. However, if the runner is going at constant velocity then there is no acceleration and thus no force.
In regards to air resistance, it's negligible (unless maybe if there is a strong head wind, though this affects the speed of the runner more than the pole fall). The speed at which everything is occurring is slow enough that all of the air flow around the pole can be considered laminar (smooth). In fact, its so slow that this can most likely be described using velocity potential theory. In velocity potential theory there is no net drag on an object in potential flow (which is what the flow around a pole moving that slow is).
To push my point home though, I'll calculate the Reynold's number. The Reynold's number is a dimensionless constant that describes how laminar or turbulent a flow is. If the flow is laminar then any air resistance can be ignored. Flow is considered laminar if the Reynold's number for the flow is less than about 2000. The Reynold's number can be calculated from the following:
Reynold's Number = (density)*(flow speed)*(diameter)/(dynamic viscosity)
For air, (density = 1.2 kg/m^3), (dynamic viscosity = 18.27 Pa-s) [Pascal seconds = N*s/m^2]
The pole is about 3 inches thick so (diameter = 3 in)
The runners were running at about 7.6 m/s so (flow speed = 7.6 m/s)
Calculating this we get the following Reynold's number:
Reynold's Number = (1.2 kg/m^3)*(7.6 m/s)*(3in)/(18.27 Pa*s) = 0.038
Obviously this is a lot less than 2000 which means that the flow is really laminar. Therefore air resistance on the pole is negligible. Air resistance on the runner is not though.
So yea, I hope that clears it up. I posted some sources you guys can take a look at below. Thanks for reading!
http://id.mind.net/~zona/mstm/physics/m ... Frame.html
http://en.wikipedia.org/wiki/Reynolds_number
http://www.media.mit.edu/physics/pedago ... acles.html
http://en.wikipedia.org/wiki/Viscosity
http://www.diracdelta.co.uk/science/sou ... ource.html