Is there a final answer to the classic question of ants climbing ropes?

Yes, in the end, it is a harmonic series, which can be climbed because it does not converge. It is because the rope is stretched so that the ants climb correspondingly increase.

Check out the book: Mathematical Paradoxes, which should have a lot to wonder.

It seems that it can be, because the rope is constantly stretching, not to say that it is connected out! In other words, it's not a new rope from the B end! So if you can't get there, then the ants can't even reach the midpoint of the rope when it's 1 meter, according to what you said, it's all at the place of 9 10, and it will definitely reach the final destination!

In fact, the actual speed of the ant is not 1cm s because the rope becomes longer, so the speed of the ant changes!

Isn't that the equivalent of a pursuit problem? Set point A as the origin of the coordinates, point B as a moving point, at this time at time t the position of the ant is 1 * t, and the position of b is 100 + 10 * t, the problem is to ask whether there is t, so that oa = 1 10 * ob (should not refer to the rope on the 9 10 place, that obviously can not reach),

Oh, I misunderstood the meaning of rope stretching...

Yes. The meaning of the title is that the rope goes up. If yes, then 1m 1cm=100s.

If the rope becomes longer, it will never reach because the rope grows faster than the ant's speed.

Did I get the question wrong?

Yes, 1, if the full length of the rubber band is set to 1, then no matter how long the rubber band is stretched, it is 1, and the result of elongation is to reduce the speed of the ant to the original 100 (100+100t)=1 (1+t) 2. The initial velocity of the ant is the full length, (according to the full length of 1, that is, 1/10,000th of the total length) 3. The speed of the ant at time t is 4. The path that the ant has traveled in a tiny period of time dt is ( 5. The distance from time 0 to time t is ( So the distance traveled by the ant is Because the full length is set at 1, let the above equation = 1 solve this equation 1+t=e 10000 t=(e 10000)-1=seconds=years.

Yes, divide the rope into 100 parts, each part is 1m, the rope is stretched by 100m at the end of the first second, because it is an elastic rope, so it is equivalent to adding 100m to each part of the 100m 100 parts, that is, dao1m, at the end of the first second, the ant climbed 1cm, and the 1cm climbed became 1cm+1m, which is 101cm, so the rest of the distance is 100m+100m-101cm, which is 19899cm, and so on.

Definitely climb to the exact process has to go through a lot of calculations, and I don't have time to calculate it right now.

10000 seconds.

Suppose the ant goes from point A to point B, (think of the rubber band as the line segment AB, which is 100 meters long = 10,000 cm).

According to the title, every second passes, the ant walks 1 centimeter, and AB is elongated by 100 meters, but because the position of the ant remains unchanged in the elongation, therefore, assuming that AB has 10000 segments, every second, the ant advances a section, so the ant needs 10000 1=10000 (seconds) to go to point B, that is, to climb to the other end.

Let's say the ant can crawl in x seconds.

Ants travel meters in one second because the length of the rubber rope increases at a constant speed, meaning that all parts increase at a uniform speed. Then the distance traveled by the ant x seconds is multiplied by x squared.

The length of the rubber rope is 100+100x after x seconds

So some squares = 100*(x+1).

x is approximately equal to 10000

It can never be, note that here "at the same time the rubber rope is evenly stretched at a speed of 100 meters per second" means that the rubber rope will be evenly thinner and the place where the ant is standing will continue to lengthen to both ends, so if the ant does not move, the ratio of the distance from the beginning to the ant to the end of the ant remains unchanged. The speed of the ant is meters per second, and the speed at which the rubber rope is stretched is 100 meters per second, of course, it is never the same.

The first second to climb over the entire rope.

Crawl in the second second.

.Crawl in the xth second.

To climb in x seconds, you must.

(The reciprocal of the natural number is called the harmonic sequence.) People have been studying it for hundreds of years. But so far there is no formula to get the sum of it, just an approximation of it (when n is large):

1+1/2+1/3+..1 n LNN + C (C = so x is about 10 to the power of 10000.

Absolutely astronomical, I'm afraid it won't be able to climb in its lifetime.

If it is elongated, it is directly divided by 100 meters by meter seconds, which is equal to 10,000 seconds.

If it is elongated, the ants will also move forward due to the tension of the rubber rope due to static friction

So it's 10,000 seconds!!

If he can't climb to the point where he gets to, then he's going to have to climb halfway there.

If he's halfway up, he's going to be halfway there.

So there is always half to climb, but there is no faster than the rope.

So can't climb.

The length of the rubber rope is that all parts increase at a uniform speed, and the ants will also go forward because of the pull of the rubber rope, so the ants are equivalent to walking on a 100-meter-long rope that will not move, that is, 10,000 seconds.

First of all, we don't think about whether the rope exists or not, it is an interesting question, the conclusion is that it can climb to the head, we can see that the elongation is 100 meters, since the ant is slower than the rope elongation, then we can assume that the speed of the ant is expanded to prove that it can climb, now let's assume that the ant's speed is 100 meters per second, yes, when it is 50 meters per second, it is also possible, when it is less than 50 meters per second, it can be climbed.

How long does it take to get 50 meters per second?

While elongating, the ants will also move 100 meters with it.

So: 100m=10000cm 10000 1=10000 (seconds).

If the rubber rope is stretched uncontrollably, then what is the difference between it and lengthening?

The rope is stretched and it has nothing to do with the ant, because the ant is not stretched, only the ant's speed is greater than the "speed of the rope extension 2" to be able to climb to the end, so it cannot climb.

Just kidding, you can't do it in the lifetime of an ant Hehe.

You'll never be able to climb the other side. It's like a person who walks slowly chasing a person who walks fast, not to mention that the person who walks fast is 100 meters ahead.

It's really hard.

First of all, when the rubber rope is extended, will the ants also move forward a little more?

Second, the rubber rope can't be stretched indefinitely, right??

Looking forward to the answer

When you climb to the end, you'll see the hell.

It's hard enough, let's announce the answer!

Assuming that there are x children with x people, ** is y yuan per person.

A's ** is y+

B's ** is.

When the two companies of A and B are equal, that is, calculate x=30, so when the number of children is greater than 30, A is more preferential than B.

The y in the title doesn't really matter, when the two formulas are equal, y can be reduced.

This week, the teacher assigned an essay topic for writing about little bugs. Today, my dad and I went to the park to observe the little bugs.

Suddenly, I noticed several ants crawling on the ground. "Dad, there are a lot of ants here," I said in amazement, "and observe the ants today." Can you help me find a fly?

Okay! "Dad went and fetched a fly, and put the fly with a thin branch, and then put the fly where there were ants, and then pressed the branch through the fly with a stone. After a while, an ant "scout" came, sniffed with his nose, moved with his antennae, and then, circling the fly a few times, pulled the fly again, but could not pull it, and he burrowed back into the hole.

I thought he was gone, but after a while, a little ant came up, no, two, three ......A large swarm of ants crawled in, and they pulled and lifted, but they still couldn't lift it. Because the flies were crushed by Dad with stones. Immediately, an ant went back to move the rescuers.

This time, he called the "big-headed general". This "general" is twice as big as the other ants, and has a large pincer in its mouth, which makes it very powerful. "Little ant, what's the matter with you?

General, the prey out there is too big, and we need you to break it down before we can move it. "Oh, you lead the way! The little ant immediately brought the "general" to the prey.

The general "expertly climbed onto the fly's back and easily cut off the fly's wings with large pliers." An ant immediately lifted its wings back into its burrow. Then, the four ants immediately lined up in two columns and straightened the fly's legs, "General, cut off this leg!"

Okay", "click", the leg was cut off, and the two ants carried the leg away, and on the way, one ant said to the other: "Hey, such a little leg, it takes two people to lift it?" Look down on me.

You go and do your work, I'll lift it when I come alone. When I saw this scene, I couldn't help but wonder: "A monk carries water to drink; Two monks carry water to drink; The three monks had no water to drink. The correctness of this age-old saying.

The general "cut off the other wing, head, and tail one after another. After a while, a fly dozens of times larger than an ant was moved back to the house by the little ants.

As the saying goes: "When the hearts of the people are united, Mount Tai moves; People's hearts are scattered, and it is difficult to move rice. "Today, I have observed the labor process of ants to truly understand the truth of this sentence.

Although the ants are small, but they always think about others in their hearts, there are good things that everyone can share together, as well as their solidarity and perseverance, compared to us humans, shouldn't we learn something from the little ants?

Ants can climb to the other end. Because: as the rubber rope is elongated, the position of the ant moves forward accordingly.

That is, it has nothing to do with whether the rope is stretched or not. The ants, on the other hand, crawl forward. The speed of the ant should be the speed at which the rope is stretched plus the speed at which it crawls on its own.

So it is possible to climb to the other end.

Yes! With each point the ant moves forward, the rubber rope in front of him stretches more slowly (relatively) because the stretch is even

1. If the full length of the rubber band is set at 1, then no matter how long the rubber band is stretched, it is 1, and the result of the elongation is to reduce the speed of the ant to the original 100 (100+100t)=1 (1+t).

2. The initial velocity of the ant is the full length, (according to the full length of 1, that is, one ten-thousandth of the total length) 3 The velocity of the ant at time t is.

4. The path traveled by the ant in a tiny period of time dt is (5. The distance traveled by the ant from time 0 to time t is (

From 0 to t integrals because (

So the distance that the ants have traveled is.

Because the full length is set at 1, let the above equation = 1

Solve this equation 1+t=e 10000

t = (e 10000) - 1 = seconds = years.

This problem is equivalent to summing harmonic series.

It is divided into 2 parts, the first half [0,1) and the second half [-2,2].

The whole function is bounded on [-2,3).

Or directly there are 2 bounded functions of the sum bounded.