"Lao Zhang, why are you still in a hurry? They must not be allowed to think about it again. It's easy, isn't that a genius who looks down on you Class 1! Qian Feng had a rare opportunity to ridicule Zhang Detong.

"Humph!" Zhang Detong is not uncommon to deal with him.

After a while, after the people in Class 2 discussed, Xu Dong directly stepped forward to write the topic.

"Hey. Xu Dong, which discipline is the topic. Or if you reveal it first, we'll just ask people to go up and do it. Wang Chao said with a grin below.

Xu Dong turned his head to look at Wang Chao, and said with a smile: "Don't pretend to be a big-tailed wolf, we don't bully people, this problem will be math." You Wang Dashao are usually awesome, or you can come up directly. ”

"Hey! That's fine! Since it's math, that's no problem? After speaking, he stood up and greeted the people in his class: "Brothers and sisters, how about giving this game to Wang Ye?" Noon cafeteria I please? ”

Before the surrounding classmates could speak, Zhang Detong's scolding rang out first: "Wang Chao, you speak well to me!" Do you want me to call you Lord Wang! Still have a lunch in the cafeteria? You're going to lose today, and I'll leave you without food for three days. ”

Wang Chao was criticized by Lao Zhang, and immediately sat down honestly like an eggplant beaten by frost.

"Whoever told you to sit down, roll me up and do the question. Do you have to let me call you Wang Ye too? Can you please go up? Lao Zhang said hatefully: "If you are a man, you have to do it when you say it." Lest someone have an excuse to lose. ”

After speaking, he squinted at Qian Feng.

"Hey! Old ~ Teacher Zhang, you can take a look. Wang Chao was so excited that Lao Zhang almost shouted.

Everyone below held back their laughter, and Zhang Detong's face was pale. You can't give Wang Chao a little bit of color, this is the owner of a dyeing workshop with a little color.

When Wang Chao came to the podium, Xu Dong had already written the inscription on the whiteboard:

Let the function y(x)(x≥0) be derivable of the second order, and y'(x)>0,y(0)=1.Over the curve y=y(x) at any point P(x,y) as the tangent of the curve and the perpendicular line of the x-axis------。

The area of the triangle enclosed by the two straight lines and the x-axis is denoted as S1, and the area of the curved trapezoid with y=y(x) as the edge of the interval [0,x] is denoted as S2, and 2S1-S2 is always 1.

Find the equation for y=y(x) for this curve.

Wang Chao took the black pen and said with a smile: "That's it? Your level of writing is too low. After discussing it for so long, you made such a thing out? Look at it! ”

After speaking, he began to write without thinking:

Let the tangent equation for the curve y=y(x) at the point P(x,y) be Y-y=y'(X-x)，

Its intersection with the x-axis is (x-y/y',0).

-------

According to the known conditions 2S1-S2=1, there is

y2/y'- y(t) dt=1，

Substituting y(0)=1, there is y'(0)=1.

The derivatives of x on both sides of the equation and simplification yields yy''=y'2,

-------

Therefore, the equation for finding the curve is y=ex.

When he finished writing, he turned around and threw his pen on the podium. Domineering said: "That's the difficulty? I was able to solve it in my freshman year of high school. Do you have any sincerity in Class 2? Look down on us? ”

"Cut!" There was a boo below.

To say that the first year of high school can solve this problem, Wang Chao is definitely bragging.

Wu Zhe smiled below, this kid's math skills are really good. Gently touched Huang Minghai beside him and said, "How many of you estimate in this class can do it?" ”

Huang Minghai frowned and pondered: "Don't look at what Wang Chao said lightly, I estimate that there are no more than ten people in the class who can make this question." I estimate that there are no more than three people who can do it as fast as Wang Chao. Our class is stronger than Class 2, and we have the kind of special strength in each subject. In fact, this competition method, Class 2 suffers a big loss. ”

Wu Zhe nodded, there are gold medalists in competitions in every discipline.

Don't say it's class 2 today, as long as the students of the same class come over from all over the country, it's still the rules of the competition. Then no one can bargain on this group of people.

"Old money, or you can let people go up first. We can also tell you the type of question. Zhang Detong saw that Wang Chao easily solved the problem, and immediately said to Qian Feng.

"Hey! Don't say you don't know how cheap your class is? Children compete, what do you say you are an adult to participate in? ”

Good guys, who was triumphant when they first came in? This is not the right form. Is it just the little guy who competes? Zhang Detong was a little speechless at Qian Feng, you scoundrel is about to catch up with Wang Chao.

It's the turn of class 1 to come up with the questions, this time in physics plus math:

When a certain detection instrument is sunk into the sea from a ship, the functional relationship between the sinking depth y (calculated from sea level) and the sinking speed v of the instrument needs to be determined according to the detection requirements. Under the action of gravity, the instrument sinks straight down from the rest of the sea level, and is also affected by drag and buoyancy in the sinking process. Let the mass of the instrument be m, the volume be B, the specific gravity of seawater be ρ, and the resistance of the instrument is proportional to the sinking velocity, and the proportion coefficient is k(k>0).

Fortunately, there are still a few great gods in class 2, and in the bumps and bumps, they finally calculated the answer as: y=-m/k v-m(mg-Bρ)/k2 ln? (mg-Bρ-kv)/(mg-Bρ).

The response of class 2 is faster, and it is directly a question of comprehensive subjects. If you can't get it alone, then don't think about it.

It is said that there are five questions, but except for the time of the first question is slightly shorter, the next questions take more time than the other. The competition started in the morning. By the time the last question was asked, it was already afternoon. In the middle, lunch is taken to go out to eat, and of course there are also people who ask someone to bring food.

The first four questions are all considered to be passed, and the difference between the two classes is in the speed of answering. This is also something that can't be helped, this kind of competition, in fact, is more powerful than the kind of competitive players in Class 1.

The last question, class 1 comes out first, and the question stem given is very simple:

A uniform cylinder rolls down from an inclined plane (without slipping).Mass M radius R.Find its kinetic energy when the angular velocity is w.

Wu Zhe was a little surprised, which ghost did this question. It looks very simple, but if you are not careful, you will step on the trap.

"Who came up with this question? Too bad? Wu Zhe couldn't help but quietly ask Huang Minghai next to him.

"Ugh! Is it damaged? It's okay," Huang Minghai said a little hesitantly.

"You can't do it, right?" Wu Zhehu doubted.

"Hehe, you just watch the show!" Huang Minghai brought the topic over with the lake.

Why did Wu Zhe say that the question was cunning, because this question seemed simple, and after answering it, it was too late to find the error.

Sure enough, the person who went up directly used: E=1/2[I(w^2)]+1/2m[(rw)^2], rolling kinetic energy plus translational kinetic energy, and instantaneously doing circular motion with the contact point as the center of the circle.

Seeing that he finished writing, Wu Zhe patted his head, and Class 2 was over.

Huang Minghai's hand is really yin, it looks simple, but there is a logical error in it. This requires treating the cylinder as a mass and at the same time as a collection of multiple particles.

"Hahaha, Xu Dong, you have to bow to us! That's a wrong question. Wang Chao shouted happily.

There will also be people from Class 2 who reacted. When the people in Class 1 explain, they will know what is wrong. But it's useless to be annoyed.

"Wang Chao, don't be in a hurry to celebrate. Do we have one more chance to do this? Xu Dong also quickly calmed down and quickly pulled people together to think about it.

"Lao Zhang, these little rabbits seem to have a bet?" Qian Feng asked a little nervously.

"It's good to have a bet! As long as it's not gambling money, some small bets can still promote feelings! This time it's Lao Zhang's turn to be proud. The advantage is in hand, the most draws. If you can win, then you can use it from time to time this semester to make a little bit of old money, isn't it more comfortable than drinking?

"The Legend of the Fairy Tree"

"It's a bet, it's not good! Or not? By the way, aren't we talking about their thinking today? The inspection of those boys has not been written yet, you see that the competition will be stopped first, and it will be carried out next time. Why not leave it in suspense? Qian Feng pretended to suddenly remember that he was still down to business.

Zhang Detong glanced at him, you are thinking about fart. When I first came in, I heard that my class had won a game first, where was the pride of that meeting? If you want to lose now, you quit first? I can't shut the door for you!

Qian Feng looked at Lao Zhang's posture, if he didn't decide the winner today, would he not give up? Now I can only see if Xu Dong's gang can help him fight?

Class 2 discussed the questions for more than an hour. They can't help but be careful, this question is difficult to fall through the meeting of Class 1, and everyone who sees Class 1 has to take a detour that week, and no one wants to bow and salute people in public.

Or Xu Dong went up to write the question:

The spacecraft has an operating mass of 2.4 tons in a landing preparation orbit, and its main reduction engine installed in the lower part is capable of generating adjustable thrust from 1500N to 7500N, and its specific impulse (that is, the thrust generated by propellant per unit mass) is 2940 m/s, which can meet the control requirements for adjusting the speed. Attitude adjustment engines are installed all around, and after the thrust direction of the final reduction engine is given, various attitude adjustment control can be automatically realized through the pulse combination of multiple engines. The intended landing site of the spacecraft is 19.51W, 44.12N, and the altitude is -2641m.

In the case of high-speed flight, the key issue to ensure the accurate soft landing in the predetermined area of the moon is the design of the landing orbit and control strategy. The basic requirements of its landing orbit design: the landing preparation orbit is an elliptical orbit of 15km at the perilunar point and 100km at the apogee; The landing orbit is from the perilunar point to the landing site, and the soft landing process is divided into six stages, which are required to meet the state of each stage at the key point. Minimize fuel consumption during soft landing.

(1) Determine the position of the perilunar point and the apogee point of the landing preparation orbit, as well as the magnitude and direction of the corresponding velocity of Chang'e-3.

(2) Determine the landing orbit of Chang'e-3 and the optimal control strategy in six stages.

When Xu Dong finished writing, not only everyone in Class 1 was stunned, but Zhang Detong, Qian Feng and Wu Zhe were all dumbfounded. In order not to lose, I don't want to lose my face. Wu Zhe couldn't think of anyone in the class who could solve this problem in an hour.

It's all cheating.

"Xu Dong, you guys are going too far, right?" Huang Minghai, who is the best in physics, stood up and said.

"Hey, can you solve it? We've come up with a problem, and it's a bit difficult, but don't pick and choose. ”

Class 2 will die and the pig is not afraid of boiling water, and the topic is difficult to explain, but if you lose, you will admit that it is not as good as Class 1.

", is that a bit hard for you? Feel your conscience and ask yourselves, which of you has the ability to solve it in an hour? Huang Minghai was not convinced.

"Don't say so much? Okay? If not, then we're tied! There was a 2nd class shouting.

", isn't it time yet?" Class 1 refuses to give up just like that, and is working hard.

"Old Qian, this is the student you teach? Learned to cheat and play tricks? What did I learn from you? "Lao Zhang, this will have something to say.

Qian Feng's face was also flushed, and he scolded in a low voice: "I'll clean them up later." ”

Wu Zhe said softly at the bottom: "You divide labor and cooperate, don't finish the problem alone, if one person has one link, is it possible?" ”

Huang Minhai understood in seconds, and immediately shouted loudly: "The spacecraft landing preparation orbit equation, I will solve the corresponding speed of the apogee and perilunar points." ”

Wang Chao immediately said: "Boss, you don't need to calculate, you can coordinate the parameters we need to calculate and need." Leave what you just said to me. ”

"Good!" As soon as Wang Chao said this, Huang Minghai knew that Wang Chao was afraid that others would not have the idea to solve the problem, and it was the best choice to have him as the coordinator.

After thinking about it, he continued to say in a loud voice: "The landing orbit and the landing coordinates are calculated together, who will come?" ”

"Leave it to me!" Shen Zhiwen said quickly beside him.

"The relative position of the perilunar point to the center of the moon."

"I'm coming!" The relay began later.

-------

Apogee Point Coordinates

"Mine!"

"Dynamical Equations and Guidance Laws for the Phases of a Soft Landing."

"Mine!"

--------

Contiguous Safe Zone Calculation

"Mine!"

--------

Almost everyone in Class 1 was assigned a task. Huang Minghai would no longer sit in his place, and soon came to the blackboard in front of him and began to draw a table, dismantling the goals of each small piece into numbers and filling in the grid above.

After doing this, he began to map the whole process of thinking to make people clearer, so that the people below could know what purpose their calculations were aimed at.

Wu Zhe looked sideways, and Huang Minghai's level in aerospace made him very surprised. There is also the kind of crispness and unfazed change. No wonder he was able to achieve the position of deputy chief engineer later.

"Boss, the relative speed of the apogee and perilunar points has been calculated." Wang Chao's first report.

"Okay, you can help others check the calculations later, you can't make mistakes, we have to go through it once this time." After speaking, he ticked Wang Chao's taskbar numbers on the form.

"Report, the coordinates of the apogee point are determined!"

-----

"Report, safe zone calculated!"

-------

"Report, the spacecraft landing angle is determined."

------

As the reports sounded, more and more numbers in the charts were ticked.

Finally, the last data calculation is complete. Huang Minghai looked at the time, there were still 3 minutes left and an hour. Immediately get up and put together all the data. I began to write on the whiteboard.

"Huang Minghai, don't write it! We throw in the towel! Congratulations! Xu Dong stood up and lost, but he was convinced.

Wu Zhe stood up and didn't speak. Just "Smack!" Syllable! Syllable! Then everyone stood up and applauded Huang Minghai and himself.

The pride in Zhang Detong's eyes couldn't be hidden. Staring at the students in his class, his eyes were a little rosy. Just now, everyone united and cooperated, and it really calmed him, and the whole person was like electricity. There are all kinds of emotions such as excitement, pride, and relief.

The applause stopped, and Zhang Detong shouted: "We won!" I'm so proud of you! ”

Class 1 cheered again.

It was already dark outside, and Wang Chao shouted loudly: "Dinner, let's go, have dinner together." I'm a treat! ”

Zhang Detong and Qian Feng didn't stop them and let everyone go back.

After everyone left, Zhang Detong spoke: "Old Qian, do you accept it?" ”

Qian Feng sighed and said, "Serve!" The talent of General Huang Minghai! ”

"Hahaha! Let's go, I'll invite you to drink! Zhang Detong laughed heartily.