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Posted by amits at Feb 04, 2009 07:51 PM
Course- History of Science
Assigned on- Jan 28, 2009
Submitted on-
Submitted by- Amit Sharma

Question- What is Zeno's paradox?
Answer- Zeno was a great supporter of Permenides's doctrine of “all is one”, according to which- "the belief in plurality and change is mistaken" and that "motion is nothing but illusion". In support of Permenides, Zeno created eight paradoxes.
 One of the most famous paradox is-
“Achilles and the tortoise” . It states, “In a race, the quickest runner can never overtake the slowest, since the pursuer must first reach the point whence the pursued started, so that the slower must always hold a lead.”
 This paradox can be understood in simpler words as, suppose in a race, achilles allows the tortoise a head start of 100 meters. If we suppose that each racer starts running at some constant speed (one very fast and one very slow), then after some finite time, Achilles will have run 100 meters, bringing him to the tortoise's starting point. During this time, the tortoise has run a much shorter distance, for example 10 meters. It will then take Achilles some further time to run that distance, in which time the tortoise will have advanced farther; and then more time still to reach this third point, while the tortoise moves ahead. Thus, whenever Achilles reaches somewhere the tortoise has been, he still has farther to go. Therefore, because there are an infinite number of points Achilles must reach where the tortoise has already been--he can never overtake the tortoise.
 This paradox may be solved quite easily now by applying the concept of relative velocity, but in past this had created a lot of debate and confusion amongst philosophers. It can be solved in following way-
Suppose the actual velocity of tortoise (u) is 10 meters per second, while that of Achilles (v) is 100 meters per minute. The relative velocity of Achilles to the tortoise (v1) is then 100 – 10 =90 meters per second or 90/60 = 2/3 meters per second. So with this relative velocity the time taken by Achilles to catch the tortoise is 100 meters/2/3 meters per second = 66.66second or 1 minute and 6.66 seconds.
Now, to calculate the distance at which both the Achilles and the tortoise will meet, we can divide the actual velocity (v) with the time of meeting i.e. 100meters per minute / 1 minute 6.66 seconds or, 5/3 feet per second / 66.66 seconds =111.11 meters.
Thus, we find that the Achilles will catch the tortoise at a distance of 111.11 meters from the start point at 66.66 seconds.