Turtles and people race, let the turtle run 1000 meters first, why can t humans catch up with the tu

The turtle is one of the slowest walking creatures in the world, crawling at a speed of kilometers per minute, in daily life, we often use the turtle to describe a person who does things slowly, but if people and turtles compete, people may not be able to beat turtles.

In the famous fairy tale "Tortoise and Hare Race", the proud rabbit falls asleep in the middle of the race, although the tortoise crawls slowly, but in the end the tortoise wins the race, the meaning of the tortoise and hare race story is to warn people not to be too arrogant, many people think that the tortoise cannot beat the rabbit.

But the truth is that even if the race is not against a rabbit but a human, humans may not be able to beat the speed of a tortoise, and the famous Achilles paradox is a good proof of this.

In the 5th century AD, Zeno published the famous Achilles paradox, in which Zeno proposed that a turtle should wait for a kilometer, that is, the turtle was a distance of a thousand meters ahead of humans, and then humans would start running.

It stands to reason that a thousand-meter gap is not too far for humans, and humans can still catch up, but Zeno's paradox gives a different view.

Suppose a person runs a kilometer in 6 minutes, and the person is 10 times faster than the turtle, then when the person runs to the position of a thousand meters, the turtle has already walked 100 meters, and when the person runs to the 1100th distance, the turtle has walked 10 meters, and the person can only end up approaching the turtle indefinitely, but can never exceed it.

The Achilles paradox seems to be well-founded, but some people believe that even though time and distance can be divided infinitely, space cannot be divided indefinitely, so the Achilles paradox is not valid.

And in the Achilles paradox, we seem to see a similar example of the expansion of the universe, human beings have been chasing the end of the universe, although it is still too early for human beings to get out of the galaxy, but in addition to human beings, will there already be extraterrestrial civilizations exploring the universe?

In terms of time, extraterrestrial civilizations were born much earlier than Earth, so their technology may be much more advanced than humans, and perhaps aliens have already touched the edge of the universe.

But as the story in Achilles' paradox goes, humanity and other civilizations may be infinitely close to the edge of the universe, but they will never be able to step out of it.

Because since the moment the universe was born, the universe has been expanding all the time, and the speed of the universe expansion has even exceeded the speed of light.

I think it's a paradox, from a scientific point of view, the turtle and the human race, even if the turtle is asked to run 1000 meters, and then the person chases it, the turtle can't outrun the human.

This is the famous Zeno paradox, because in Zeno's hypothesis, humans run after the turtle, and the distance between humans and the turtle is constantly shrinking, but the turtle is also constantly advancing in the pursuit of humans, creating the hypothesis that it will never be able to catch up.

This is a race against tortoises and rabbits. The rabbit ran faster than a man, but it didn't catch up with the tortoise, not to mention that the tortoise ran a thousand meters first, and we were so tired and panting for a thousand meters.

Humans are very intelligent and fast, but they are always attracted by the scenery of the path, and they underestimate the strength and perseverance of the turtle, which leads to the final failure.

Because the runway is only 1000 meters, the turtle has already reached the end, how can it still catch up with the turtle.

I think it also depends on the actual distance, if its actual distance is only a thousand meters then it is impossible for humans to catch up with the turtle, but on the contrary, if its actual distance is infinitely extended, then it will always catch up.

For mathematical calculations, their distance is infinitely close to zero but not equal to zero, which means that they will never be able to catch up with the turtle.

Underestimating the enemy is always a failure, no matter how small the opponent is, we must be ready for the battle and play seriously.

Achilles was the fastest carrier in ancient Greek mythology, but Zeno proved that Achilles could never catch up with the tortoise. The proof is as follows: Achilles started from point A to catch up, and the turtle that started from point A1 in front of him, if he wants to catch up with the turtle, he must first reach the position A1 where the turtle starts running, and when Achilles reaches the position where the turtle starts to run, A1, the turtle has already advanced some distance and reaches A2, so Achilles must first reach position A2 if he wants to catch up with the turtle, and when he runs to A2, the same problem is placed in front of him again.

Therefore, although Achilles ran fast, he could only approach the turtle little by little, but he could never catch up with the turtle.

Based on the summation of infinitely proportional decreasing sequences of numbers learned in middle school, Zeno's paradox can be easily overturned by simply listing an equation: Achilles can catch up with the turtle when he runs 1000 (1+ (1+1 9) = 10000 9 Achilles paradox meters. It is believed that the number 1+ can never be exhausted.

This is nothing more than an illusion.

Let's calculate the time when Achilles can catch up with the turtle t(1+ (1+1 9)=10t 9 Zeno said that Achilles could not catch up with the turtle, which hides the condition that the time must be less than 10t 9.

Since Achilles and the tortoise are in constant motion, there is no limit to the time of the Qing attack, and the time can easily exceed the condition of 10t 9. As soon as such a condition of 10t 9 was breached, Achilles caught up with or overtook the tortoise.

People are deluded by the illusion that the distance series 1+ seems to be inexhaustible, and they do not consider that the time series 1+ is easy to reach and exceed. But it is not good that all the sequences can be reached, so we can't look at the problem too extremely. For example, no matter how many points there are, we can't form a straight line, and we can never exhaust the number of points.

Summary. Because the tortoise was already 10 meters ahead of me before the start, when I let me and the tortoise start at the same time, when I was about to overtake the tortoise, the total distance I walked minus the first 10 meters would be equal to the distance the tortoise walked.

The turtle is 2 seconds a meter, I am 1 second a meter, and now the turtle is 10 meters ahead of me, and I am asked how many seconds to overtake the turtle.

Hello, it is a pleasure to serve you. I am a teacher Qinghuan, with 5 years of industry experience, good at the field of leisure and entertainment sedan socks, a total of more than 1216 hours of 1v1 consultation, please wait a while, I am working hard for you to sort out the answers, 3 minutes back to you

Hello, happy with your question. According to the title, I will overtake the turtle in 20 seconds.

Because the Lingchang tortoise was already 10 meters ahead of me before the start, when I let me and the tortoise start walking at the same time, when I wanted to overtake the tortoise, the total distance I walked minus the 10 meters at the beginning of the slide would be the distance that the tortoise walked.

Then first calculate the difference of the tortoise's speed is, my velocity is 1m s, let me exceed the tortoise at t seconds, and then falsely judge the bridge according to the formula 1t-10=, and solve t=20 seconds.

Xibo quietly hopes that my answer can help you Oh If you are satisfied with this consultation, can you give me a thumbs up, thank you.

I just saw a**: Put the turtle on the treadmill, accelerate for a long time, and the speed of the turtle gradually increases. After reading it, I will feel that the turtle can run so fast.

That's right, a turtle can run so fast, and if you don't push yourself, you never know your limit. We are always accustomed to living a comfortable life, and once we encounter difficulties, we will subconsciously avoid and retreat, and subconsciously think that we can't do it. The tortoise may also think that it can't run fast, and in the tortoise-hare race if the hare is not lazy, it is doomed to lose, but it turns out that the tortoise can also run fast, and if it uses this speed, the final result is not necessarily that the tortoise loses.

We are like this turtle, usually cowered in our shells, unwilling to stick out our heads, and run on all fours. I am only willing to move slowly, and I have to tell myself that I have a lot of time anyway, and I want to enjoy the moment.

Can you really spend tomorrow and the day after tomorrow so leisurely? No successful person is easy, take advantage of your youth, push yourself, and be brave enough to try and learn. Crawl out of your shell and run on all fours, a turtle can run so fast.

The turtle ran 1200 meters·· People ran 2,000 meters and more than 800 meters, right? When the turtle runs the first 100 meters, it's 1000 + 100 = 1100 meters, and the person runs 1000 meters, and the turtle runs another 100 meters, and it's 1100 + 100 = 1200 meters, and then the talent runs the second 1000 meters, so when the person runs 2000 meters, the turtle runs 1200 meters! Added:

Uh, anyway, I looked up the question just now, and I realized that you seem to have asked the wrong question, right? It must be ten times faster than a turtle, right? But it's not that for every 100 meters a turtle runs, people don't run 1,000 meters!

If a person is 10 times faster than a tortoise, and the tortoise is 1,000 meters in front of the man, then the man can't catch up with the tortoise! The journey of chasing the tortoise is arbitrarily divided into infinite segments, and it is believed that it will take an infinite amount of time to complete these infinite distances. In fact, even according to this segmentation method, it takes 1 hour to complete the first section, 10 minutes of an hour to complete the second section, and 100th of an hour to complete the third section......In this way, the time to catch up with the turtle is precisely a finite:

1+1/10+1/100+..1 and 1 9 (hours) (based on the knowledge of infinitely decreasing proportional sequences that you will learn in high school, you can rigorously deduce) This is consistent with the results obtained by arithmetic and algebraic methods. Oh.