After glancing around the classroom, Xu Chuan calmed down and started solving problems.
The orbit calculation of a space shuttle or launch vehicle is a fairly basic topic in physics, but this foundation is based on college rather than high school.
But after mastering enough high school knowledge and a certain range of university knowledge, it is actually possible to do this type of questions.
Solution: (1) From the orbital equation, we know that r near=R/1+ε and r far=R/1-ε.
The total energy E and the orbital angular momentum L are conserved quantities, then L = mυ near r near = mυ far r far = mυr
or υ=L/mr
The total energy of the system is E=C/r far+L/2mr=-C/r far+L/2mr far.
where C=GMm=mrυ
GMm/r=m(υ/r) is used here.
From the expressions of ①②③ and C, we can get
R=L/mrυ
ε=√1+2EL/mrυ=√1+2EL/mrυ.
At this point, the first question is over. From the perspective of an ordinary high school student, writing down the orbit parameters R, ε can probably be placed as the second question in the final question of the college entrance examination.
But for the contestants participating in the CPHO National Finals, this is just an appetizer.
As the final question, the purpose is naturally to screen out the gaps.
And this year’s question-writing team played a little trick.
"How is that possible! Which school does this little guy go to? It has only been an hour, and the first and second questions have been completed? Did I remember the time wrong?"
Thinking about this, Qiu Chengan raised his head and glanced at the big round clock hanging on the blackboard in the classroom. The hands pointed to ten o'clock, clearly telling him that it was only one hour and ten minutes before the exam started!
This made him swallow his saliva and lower his head to look at the name on the test paper.
In this way, starting from the first question and then moving on to the second question, each question will be more difficult than the last, giving people the illusion that the next three and four questions are more difficult.
"What the hell? He started from the first question? And he finished the first two questions so quickly?"
As for these three mobile invigilators, they are usually preempted by the professors of the question writing team themselves.
After writing the first question, Xu Chuan continued writing and began to answer the remaining questions two, three, four, five, six, seven and eight.
Someone squatted quietly next to him, and everyone was confused.
Sometimes when answering questions, there is often just a little inspiration. When the inspiration comes, I eat three pounds of bananas, and the flow is endless; when the inspiration stops, it is like eating three pounds of peppers, and it hurts.
Xu Chuan looked confused, somewhat confused as to what this man did.
This year's national finals topic was chosen by him and several other members of the expert group, and he was very clear about the difficulty of the topic.
His behavior just now can actually be considered as interfering with students' answering questions, after all, it caused so much noise.
This can also be regarded as a test of students' adaptability and leadership ability.
"Oh, another one who is obsessed with the first question, can't his mind be brighter?"
So he is looking forward to how this year's candidates will respond to this situation.
Just like this middle-aged man running around in various classrooms carrying a thermos cup.
On the side, Xu Chuan, who was concentrating on writing answers, suddenly felt something approaching from his surroundings. When he looked up, a middle-aged uncle holding a thermos cup had his head stretched out on his table.
The middle-aged invigilator man, who was swaying and holding a thermos cup, walked to the side of Xu Chuan, took a closer look, and praised in his heart:
There are two invigilators per classroom for the National Examination, one in front and one behind, to prevent cheating. At the same time, three mobile invigilators are also set up to prevent unexpected situations such as candidates fainting.
They're leaning over the table to watch other people answer questions. What's wrong?
He shook his head, ignored the somewhat nervous middle-aged teacher, and continued to answer the questions.
But he really couldn't hold back his curiosity.
If you pass the exam, you can be directly admitted to major prestigious schools, recommended in advance, or even join the training team to represent the country and compete with candidates from other countries.
Xu Chuan was startled, exclaimed, and quickly turned his head to one side, away from the middle-aged uncle who was squatting next to him silently.
Qiu Chengan was holding the thermos cup in disbelief. He leaned down slightly and looked at it. The answer sheet on the table was densely filled with writing. It looked like he had indeed started from the first question.
After saying that, he left his back to everyone and quickly slipped out of the classroom.
This year's questions are slightly more difficult, but the most difficult of the four questions is only the finale. In fact, the first question is not something that most students can't solve, but it will take more time and energy.
This exclamation immediately attracted the attention of all the candidates in the entire classroom.
"Is this Cao Wei from Master P's No. 1 Middle School? Not bad. He knows how to avoid the first two questions and do the latter first."
Qiu Chengan looked embarrassed, but he had already seen the name on the test paper, coughed, and pretended to be serious: "Do the questions well."
They placed the penultimate question on the first question and the final question on the second question.
"Fuck!"
In the examination room, a middle-aged invigilator carrying a thermos cup slowly walked around the classrooms, inspecting each candidate's problem solving while invigilating the exam.
If you stick to the first and second questions, three hours will not be enough. As a result, there will be no time to answer the third and fourth questions that are much easier later.
The total game time is only three hours, so you have to hurry up.
It's the invigilator, right? I've never seen an invigilator like this?
After all, it is the national finals, so the pressure is still very high, no less than the college entrance examination.
"Hey, this guy is pretty good. He's almost finished the third question."
Being stared at by dozens of people in the classroom, Xu Chuan looked uncomfortable, but he himself was shocked.
After coming out of the classroom, Qiu Chengan was too embarrassed to go back in.
"Huh? No, this guy has finished the first three questions?"
"Which school does this kid go to? He stuck to the first question and solved it so slowly. If he goes on like this, he won't have time to do the rest."
Under such high pressure, students faint almost every year.
If some students read the entire test paper and study it first, they will definitely discover this little trick.
A student who could finish three big questions in one hour was still the three most difficult questions. This simply refreshed his knowledge.
You must know that the second big question was solved by him and another expert. It is very difficult and cannot be solved by ordinary high school students.
Now it was solved in one hour. No, it was less than an hour. This guy solved three questions in one hour, which made him doubt his own level.
Are the questions this time too easy?
Qiu Chengan was probably thinking this, but he was a little puzzled.
For this final question, he had clearly checked it with the other professors on the question-writing team and carefully selected it from more than a dozen questions.
They all agreed that if they want to solve this problem, even if they are graduate students, it will take at least one or two hours.
