I failed a course, and the system became my study supervisor.

Chapter 44 Study of the Ping Pong Rocket Problem
After thinking it through, Xu Ling no longer paid attention to the problem of the drone battery and put it aside.

What we need to prepare for now is the mock confrontation scheduled for May 15th.

Since Xu Ling's group was on the opposing side, if they did not have a thorough understanding of Group 1's questions, they would have no chance of winning.

Xu Ling already understood the principle of the table tennis rocket very clearly. It was nothing more than a process of energy conversion.

But the original question emphasized the height at which the ping-pong ball was thrown, and the given parameter was the volume of water.

If we think about it simply, what can change is the shape of the container. In the simplest terms, containers are all cylindrical.

So is it better to have a cylinder with a large radius and a wide and flat shape or a cylinder with a small radius and a long and thin shape?

In fact, these issues were raised in the report of the discussion group, but Xu Ling and other people in the group were attracted by the various complex formulas in it and did not pay attention to those issues at all.

So, it seems that if you want to understand the quantitative relationship of the conversion of liquid kinetic energy into ping-pong ball kinetic energy, you must do a theoretical analysis and simple experimental verification yourself.

……

The next afternoon, Xu Ling gathered everyone in the group together.

The purpose is simple, which is to use the power of as many people as possible to solve this problem quickly.

"With the simulated confrontation imminent, we must understand the principles and focus of the experiment and the strategies the other side might adopt."

Xu Ling said solemnly.

"Well, let's start with the simple principles. Who can explain it?"

Xu Ling continued, his eyes mainly looking at Liang Xiuyuan and Huang Yunfeng.

The two people who were swept by the gaze became a little nervous for a moment, lowered their heads and seemed to be thinking constantly, but did not speak for a long time.

In the end, it was Qin Qin who explained it clearly.

"Energy conversion! How can you not answer such a simple question? This is the most basic principle, we must understand it."

Xu Ling spoke seriously to Huang Yunfeng and Liang Xiuyuan.

The two nodded heavily.

It wasn't that Xu Ling wanted to make things difficult for them. Team competitions involve discussions between the two sides, and everyone had to participate. If they didn't even understand the most basic principles, how could they not say a word during the discussion?

Even if they don't say anything, the commentators will still ask them questions?

Shaking his head, Xu Ling continued to ask: "Do you have any ideas for analyzing this problem?"

In fact, it would not be too difficult for Xu Ling to complete the theoretical analysis of this problem, but what he wanted to do was not to rely entirely on himself, but to guide his team members.

After all, a single tree cannot make a forest.

After the group pondered for a long time, Ji Yun was the first to speak:

"Well... although this problem doesn't seem difficult from a macro perspective, the sinking of the ping-pong ball in the water, the generation of the jet in the water, and the rise of the ping-pong ball after leaving the water are not simple movements.

I think it should be analyzed in two parts: one is the interaction between the water and the ball, and the other is the movement of the ball in the air."

Listening to Ji Yun's description, Xu Ling also made a simulation in his mind and immediately made arrangements:
"Yes, Ji Yun, that's a good point. There's nothing wrong with this analysis. Let's try to analyze it. First, separate the process in the water from the process in the air. Ji Yun, Huang Yunfeng, and Liang Xiuyuan, try to analyze the movement of the ball after it leaves the water. You can ignore the ball's rotation for now."

The movement of the ball in the water was naturally completed by Xu Ling and Qin Qin.

Because motion in water is much more complex than in air. Not only must the generation of jets be considered, but also complex issues like wave-flow focusing effects must be considered. Buoyancy cannot be ignored either. Qin Qin's primary task was to find the necessary literature for Xu Ling, while also providing preliminary assessments and addressing any gaps in Xu Ling's analysis.

Soon, Xu Ling began his analysis, his pen moving across the paper, one mathematical symbol after another appearing on the page:
As the ball sinks, the container is used as the reference system. In the Z-axis direction, Newton's second law is applied: ma=Fa+Fγ+Fd+Pa.

At the same time, since the mass of the ball is very small, the ratio of the ball's acceleration to the added mass force is much less than 1. This shows that the inertia of the ball can be ignored relative to water.

After a series of approximations and specific substitutions of various expressions, and then from the integral relationship, the vertical falling depth of the ball can be obtained.

Finally, through computer simulation, Xu Ling was surprised to find that within a certain height range, the theoretical and simulation results were consistent.

Everything was going smoothly for Xu Ling, but on Ji Yun's side, the three of them were already in a state of panic.

Although Ji Yun had a general idea, she felt helpless when it came to every specific detail.

For example, the jet may not be generated directly towards the ball, so the collision is not a head-on collision, and a small deviation angle becomes a torturous parameter.

Not to mention air resistance and the change in mass of the ball due to water.

While Qin Qin was looking for literature, Xu Ling decided to give Ji Yun and the other two a simple guide.

"If the velocity isn't along the Z axis, what should I do?"

Xu Ling said this half-jokingly.

Ji Yun scratched her head awkwardly, and a blush instantly appeared on her cheeks.

"It's easy to solve. If the direction is wrong, then we can just decompose it. Decompose the speed into the Z-axis direction and study the speed in the Z-axis direction first.

Then, we found that this deflection is not actually obvious, and we can deal with it approximately by adding a correction term to the final result. "

Xu Ling gave a hint.

Yup!

Vector decomposition!
How come I didn’t expect this?
Ji Yun seemed a little annoyed, but she had to admire Xu Ling even more.

He is obviously younger than me, how come he is so awesome?

Huang Yunfeng and Liang Xiuyuan also reacted at this time and immediately started gesturing in the air with their hands.

……

Many hands make light work. This saying is indeed true.

After Xu Ling fully utilized the strength of everyone in the group, it only took two days to sort out all the theoretical analyses clearly.

Even if he was asked to give a report on the spot, it would not be difficult for him.

Moreover, Xu Ling did not choose to conduct the experiment himself, but instead used a computer to perform a simulation experiment.

In this way, a lot of time is saved and the group members can have more time to discuss various issues.

These questions include guessing about the analytical thinking of a group of classmates, understanding of certain details that are easy to overlook, and anticipating possible mistakes that a group of classmates may make.

In short, Xu Ling and his team have made sufficient preparations and are looking forward to the official start of the simulated confrontation.

(End of this chapter)