The rabbit and the turtle are one of Zenon\'s paradoxes. Suppose that rabbit run

Question

The rabbit and the turtle are one of Zenon's paradoxes. Suppose that rabbit runs 10 times as fast as the turtle. Both of them will compete in who will first reach the goal of 100 meters. As the turtle is slower than the rabbit, it gets a head start of 80 meters. The paradox is that when the rabbit has sprung these 80 meters, the turtle has reached 8 meters, when the rabbit has sprung these 8 meters, the turtle has reached 8 dm. That reasoning would cause the rabbit never to reach the turtle. Examine and explain the paradox, as well as find a solution when the rabbit comes before or finishes at the same time the turtle.

Explanation / Answer

After time period t0 positions will be :- the rabbit has travelled 80m and reached the turtle’s starting point. During this t0, the turtle has moved a distance (1/10 times of rabbit) 8m.

After time period t1 position will be :- in this time period the rabbit has travelled 8m and reached the turtle’s starting point(which is after t0). During this t1, the turtle has moved a distance (1/10 times of rabbit) 0.8m.

After time period t2 position will be:- in this time period the rabbit has travelled 0.8m and reached the turtle’s starting point(which is after t1). During this t2, the turtle has moved a distance (1/10 times of rabbit) 0.08m.

Thus, after infinite time periods, the rabbit reaches an infinitely small distance from the turtle but never passes it. We know that in real life this is not how it works and the rabbit would overtake the turtle. That's why this is a paradox.

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