Restart
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When I opened my eyes, I was in a completely different place.
It was a modest, rectangular room.
Inside, about twenty kids sat huddled together at their desks.
At the front, a man was solving a simple physics problem on the board.
"Now, this problem can be easily solved using Newton's second law..."
Why am I here?
As I wondered, the scene felt strangely familiar.
This place.
The people around me.
Class 3-1? Mr. Kim Moon-ri?
It clicked.
This was the classroom where I spent my senior year of high school.
The man teaching physics at the front was Mr. Kim Moon-ri, my homeroom teacher back then.
Ah...!
I recalled the final moments before I lost consciousness.
The strange voices that had echoed in my mind.
They said I was regressing.
Regression.
In other words, going back.
Usually to a specific point in the past.
Looking at my current situation, it seemed it had actually happened.
So I'm a high school senior again? Really?
It didn't feel like a dream.
My mind was incredibly sharp and clear.
My memories of this period were vivid.
I could instantly tell who was who among the kids.
Yoon-sung, Jun-yeop, So-hyun...
Still, it was so unrealistic that I couldn't help but doubt it.
Then, a translucent message materialized in a corner of my vision.
As if answering my doubts.
[You have regressed!]
Haha.
The moment I saw it, all doubt vanished.
I was absolutely certain now.
In that case...!
A wave of excitement washed over me.
I had so many regrets in my life.
This meant I had a chance to set them all right.
And that wasn't all.
Access Authority to the Library of the Gods: Science and Technology
Please check and use the skill!
A skill?
I focused my gaze on the additional message that appeared.
A detailed description unfolded before my eyes.
Allows you to acquire any desired knowledge from the Library of the Gods. This knowledge is strictly limited to the domain of science and technology.
Cost: Karma is required...
The science and technology of the gods?!
As I read the description, the method of using the skill and its applications naturally surfaced in my mind like common sense.
It was as if a deity had directly implanted the understanding into my brain.
This was truly a skill that granted access to divine technology.
Among those technologies was the very one I had been researching.
Plasma Control System.
Instantly, the name of the searched knowledge appeared right in front of me.
A technology to control and stabilize the high-energy state of matter known as plasma. Plasma generally exists under high temperatures and pressures...
Incredible...!
However, this was merely the concept of the technology.
To unlock the actual, precise details of that knowledge, something else was required.
Karma.
A force also known as deeds or retribution.
It existed in two forms: positive and negative.
The price demanded by this skill was positive Karma.
And the way to accumulate positive Karma is by exerting a good influence.
This was measured not by human standards, but by cosmic ones.
Information regarding this also floated into my mind.
It's not entirely different from human standards.
In that case, gathering Karma shouldn't be too difficult.
I can already see a way to earn some right here.
From the teacher right in front of me.
"Now, next. Hmm... this problem is quite difficult..."
I checked the problem he was looking at.
I looked down at the textbook open on my desk.
Problem 9. There is a coordinate plane with a uniform electric field of strength E. Two particles, a and b, both with mass m, are launched from the origin...
(Note: The acceleration due to gravity is g in the -y direction...)
[Difficulty: Special]
Is this supposed to be hard?
It was slightly convoluted, but it was actually a simple problem that only required applying a few core formulas.
You just had to solve it step-by-step.
Well, I suppose I'm not a normal high schooler anymore.
As I was thinking this, the teacher shook his head and spoke.
"Why is a question like this even in here? This looks like something from an Olympiad... Let's just skip this one."
At that moment, I raised my hand.
"Mr. Kim. May I try solving that problem?"
"What? You?"
The teacher stared at me, dumbfounded.
The kids around me also looked at me as if to say, What is he talking about?
Ah, right. Normal students don't do this.
At least in South Korea, students rarely volunteer unless called upon.
Especially not to volunteer to solve a problem on the board.
Besides, at this point in time, I was the worst student in the class.
During high school, I was completely addicted to gaming.
I would stay up all night playing, sleep through school, and never study.
It was the same even in my senior year.
Eventually, I had to retake the college entrance exam just to get into a mediocre university.
And now, someone like me was volunteering.
Bewildered, the teacher asked me.
"Uh... did I hear you correctly? Hyunwoo, you're saying... you want to solve this problem? Without being asked?"
"Yes."
"But why all of a sudden...?"
"I just think I can solve it."
"What?"
The teacher stared at me with an absurd expression, hesitated for a moment, and then nodded.
"Hmm... Alright, then. Give it a try if you want."
I picked up my textbook and walked up to the blackboard.
The eyes of the entire class locked onto me.
"What's up with him?"
"Why is he doing that?"
Naturally, none of them expected me to actually solve it.
They were just baffled by my sudden, erratic behavior.
Well, I'll just solve it.
I looked at the problem again.
Problem 9. There is a coordinate plane with a uniform electric field of strength E. Two particles, a and b, both with mass m, are launched from the origin in the same direction, making an angle θ with the x-axis, and undergo projectile motion.
The charges of a and b are 0 and -q, respectively. Particles a and b undergo an elastic collision on the x-axis, continue their projectile motion, and collide once more. Immediately before the first collision, the velocity vectors of a and b are perpendicular. If the angle that the line segment connecting the origin and the position of the second collision makes with the x-axis is ∅, and tan∅ = 5tanθ,
Find qE/mg.
(Note: The acceleration due to gravity is g in the -y direction. Ignore collision time, air resistance, and the electrostatic interaction between a and b.)
[Difficulty: Special]
The answer this problem demanded.
In other words, qE/mg was the ratio of the acceleration caused by the electric field to the acceleration due to gravity. It represented how much the motion of the charged particle in the electric field was influenced by the electric field compared to the gravitational acceleration g.
To find this, I first had to derive a formula.
Specifically, how the electric field affects the particles' motion in the x-axis and perpendicular directions.
I wrote down part of the formula on the blackboard.
I wrote in the neat, professional handwriting I had developed during my research years.
Clack, clack, clack.
qE/m * cosα = {(2Vxb - 2Vxa) * g} / 2Vya
qE/m * sinα = {(2Vyb - 2Vya) * g} / 2Vya
I heard a soft gasp of surprise from the teacher.
"Huh?"
Ignoring him, I moved on to the next step.
At the moment of collision, the velocities of the two objects are perpendicular, so their dot product is zero.
Since the two objects have the same mass, their velocity vectors are exchanged after the collision. If the time between the first and second collisions is t, the average velocity between the two collisions must also be equal, so...
I rapidly wrote down the corresponding formula.
It was almost immediately after the first set of equations.
Clack, clack, clack.
t = {(2Vxb - 2Vxa) * m} / (qE * cosα) = {(2Vyb - 2Vya) * m} / (qE * sinα) = 2Vya / g
The teacher hurriedly interrupted me.
"Wait, wait a minute. Do you actually know what that is and why you're writing it?"
"Yes, of course. It's the formula representing the time it takes for the two particles to collide, in relation to the charge-to-mass ratio, the angle between the electric field and the x-axis, and the acceleration due to gravity. Am I wrong?"
"Uh... No, you're right. You're right, but..."
Seeing the teacher's bewildered reaction, I looked back at the formulas I had written on the board.
There was nothing wrong with the equations themselves.
However...
Ah, I skipped too many steps.
I should have looked at it from a high schooler's perspective, not my own.
I added a few of the intermediate steps I had skipped.
Clack, clack, clack.
(Vxa = Vya) * (2Vxa - Vxb - Vyb) = 2V²xa - VxaVxb + VyaVyb = 0
2(2Vxa - Vxb) = 2Vxa - (qE/m) * cosα * t
-2Vyb - gt = -2Vya - ((qE/m) * sinα + g) * t
"Adding these should make it clearer, right?"
"Uh... Uh, yes."
Leaving the teacher with his awkward smile, I continued solving the problem.
This time, I explained it aloud as I went.
"Next, we need to represent the position between the two collisions. To do this, we must use the given tangent condition."
"R-Right."
"Since the time to the first collision and the time between the first and second collisions are equal, if we define the position of the second collision as (x, y), particle a moves by 2Vxa(2Vya/g) in the first collision and (Vxa - Vxb)(2Vya/g) in the second collision along the x-vector. Therefore..."
Clack, clack, clack.
x = (3Vxa - Vxb) * (2Vya / g)
y = - (Vyb * (2Vya / g) + 0.5g * (2Vya / g)2)
"Therefore..."
Clack, clack, clack.
(5Vx + Vy) / Vx = {Vyb * (2Vya / g) + 0.5g * (2Vya / g)2} / {(3Vxa - Vxb) * (2Vya / g)}
= (Vyb + Vya) / (3Vxa - Vxb)
"Next, if we assume the ratio of the speeds of a and b is 1:k and calculate..."
Clack, clack, clack.
5 = (1 + k) / (3 - k)
6k = 14
k = 7/3
"We have all the necessary values now. All that's left is to substitute this back into the formulas we derived earlier to get the answer."
The teacher stared at the board with a blank expression.
"..."
Honestly, the problem was practically solved at this point.
But I should finish it properly.
I returned to the formulas I had written at the beginning.
"Now, if we substitute this value into the conservation of momentum formula before and after the collision..."
Clack, clack, clack.
"We get the ratio of particle a's velocity in the x-axis direction to its velocity in the y-axis direction. Substituting this back into the relation between motion and the electric field..."
Clack, clack, clack.
"We get the ratio of how electromagnetism affects the motion of the particle in each direction. Finally, by substituting this value into the ratio of acceleration by the electric field to acceleration by gravity—which is what the problem asks for—we get the answer. In other words, the required answer is..."
Clack, clack, clack.
"Eight times the square root of two, divided by three. That is, the ratio of acceleration by the electric field to acceleration by gravity is approximately 3.771."
With that, I turned back to the teacher.
He was still staring blankly at the blackboard.
"Mr. Kim?"
"Huh?"
"Is the answer correct?"
"Uh... Y-Yes, it should be. No, it is correct. The answer is correct, but..."
He looked at me with a dazed expression.
He looked as if he couldn't comprehend what was happening.
"How did you..."
As he trailed off, the classroom remained dead silent.
Unlike when I had first walked up to the board, there wasn't even a whisper.
Looking around, the other kids were also staring at the board with blank expressions.
It seemed the teacher wasn't the only one in shock.
"..."
"..."
Meanwhile, several notifications popped up in front of me.
You have acquired Karma! +108
You have acquired Karma! +4
You have acquired Karma! +6
You have acquired Karma! +5
...
Total Karma: 222
Perfect.