While browsing another thread, I ran into this...
Quote:
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Originally Posted by Essex
on another lotr site many years back now it seems, we had a lot of fun, ganshing of teeth, screaming, cursing etc on how on earth movie Gandalf caught up with 1/ his sword 2/ the balrog on his trip down the unmeasurable drop from the bridge of kazad dum. unfortunately the site seemed to go into decline and vanish a couple of years back (hence why I moved onto here)
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Now, I know that at first it may seem that the laws of Physics have been violated, but upon further review, there is a very plausible explanation for all of this.
It all revolves around the concepts of
Initial and Terminal Velocity.
To make our calculations easier, we will assign the -Y (NEGATIVE Y) direction as the positive for velocity (so falling means having a positive velocity, while jumping up has a negative velocity).
We can assume that the initial velocity of the Balrog is zero, as it is found at rest before the bridge breaks under him. Yet who is to say that the initial velocity of Gandalf and his sword is zero as well?
Furthermore, as there is no reason to assume that they were falling in vacuum, there must have been a specific terminal velocity for each of the objects, Istari or fallen (as in evil) Ainur. To refresh your memories, the terminal velocity is the velocity an object reaches when the acceleration of gravity is counteracted by air friction, to give a net acceleration of zero (and thus making velocity constant).
As terminal velocity depends on friction and friction depends on surface area, terminal velocity depends on surface area. Now, we know that Gandalf fought the Balrog before they reached the bottom of the pit, so he must have somehow caught up with him, which means that the Balrog must have had a greater surface area than Gandalf. Coincidentally, this is pretty conclusive evidence that Balrogs DO have wings, as what else could give him a higher surface area? But I digress, this is not the point of this essay.
Furthermore, what about initial velocities? and how does Gandalf ever catch up with his sword? after all, the sword sure does have a smaller friction (and thus a higher terminal velocity) than the other two falling objects.
Well, we know that Gandalf DOES recuperate his sword, so there is only one possible scenario, as far as I can see. Seeing that he was going to fall, and feeling that he was losing grip of his weapon, Gandalf decided to throw it
upwards before he started falling. The initial velocity of the sword was
Negative therefore it takes a longer time for it to catch up with the old Wizzard. By then, he is able to recuperate his wits (after the shock of being dragged down by the Balrog) and he can catch his sword mid-air, and then catch up with the fallen (and falling) Ainur.
Therefore, I ought to conclude, that what we read in the book (and see in the movie) is not only plausible, but also a logical explanation.