University Physics Competition!

So this is the post about the physics competition that I promised. It’s a week late, I know – I had underestimated how much work I had put aside for the competition.

See our paper here, by the way.

The competition is comprised of two problems. You can work in teams of up to three people to solve one of the two problems. By “solve” I mean a) analyze the problem as in-depth as possible and b) write a paper detailing your analysis, all of which must be done within 48 hours. You can think of it as similar to Moody’s Mega Math challenge, but for physics (and 48 hours instead of 14). I think the competition itself is pretty new. It started last year, doesn’t seem to be very well known, and probably doesn’t give very exciting prizes. Oh well. It was pretty awesome anyway.

I decided to work with my (really damn smart) friends Matei Ionita and Yifei Zhao in Columbia’s physics building, Pupin. The whole experience was very intense. We must have slept for something like 8 hours total, but the process of solving a non-trivial physics problem with good friends was a LOT of fun. As for the results of our hard work… well, it exceeded our expectations by a wide margin.

We had decided which problem we were going to work on in the first ten minutes of the competition:

Problem B. Shooting a Basketball for Three Points

In the game of basketball, a player scores three points by successfully making a shot from beyond the three point line, which is 6.2 meters away from the basket in international games, such as the Olympics.  Suppose a player in an Olympic basketball game is at the three point line standing at a point making an angle 45 degrees to the principal axes of the court.   What initial ball velocities and spins will result in a successful shot from this point?

I’m sure every team approached this team slightly differently, but here is what we did (if you want more details, read our rough but pretty complete paper):

1. Set up the equations of motion of the ball while in the air (gravity, buoyancy, drag, and Magnus)
2. Calculate how the velocity and spin of the ball change when it collides with either the rim or the backboard
3. Write a Mathematica simulation to model the actual physical setup given
4. Analyze our data

Step 1 went by relatively quickly, although we weren’t able to take into account the effect of air viscosity on the angular velocity of the basketball. Surprisingly, even our good friend Goo G Le couldn’t help us there. Step 2 (the part of our paper on solving integral equations) was by far the most difficult part of the project. If I remember correctly, we worked on it from Saturday afternoon to Sunday at 6 am. Step 3 just consisted of tedious and painful debugging (but was pretty awesome once we got it working) and step 4 we must have spent all of 30 minutes on (the thirty minutes before the paper was due, that is).

In the end, we essentially had a (relatively bug-free) free throw simulation which we hoped was physically accurate. Here are a few pictures:

We proceeded to run the simulation tens of thousands of times (don’t you just love Mathematica?), with the basketball having a different initial state in each run. We ended up with contour plots that looked something like this:

Broadly, these contours represent the points in the domain of the basketball’s possible initial configuration space (i.e. space). The layering we see is most likely due to the distinct trajectories the ball can make; for example, the ball can go directly in, or it can hit the backboard, or perhaps the backboard and rim, etc. In other words, suppose you have a set of initial conditions that make the basketball go directly in the hoop. A small change in the initial conditions might change the trajectory drastically, which is what produces the layered structure (or at least that’s what we think).

Anyway, that’s about all for the competition. Feel free to critique our paper and/or our calculations! … just try to keep in mind that we did this in 48 hours, heh.

For my next post… hmm. I might talk about some cool extra dimensions stuff that Prof. Greene did in our QM class a few weeks ago, or I might write a bitabout some open science stuff I’ve been thinking about recently.

It’s been a while

So WordPress tells me that I haven’t blogged in months… it’s amazing how time flies in college, what with the interesting classes, people, and of course, New York City.

My courses are surprisingly interesting given my freshie status:

• Intro. to QM: Mostly cool because Brian Greene is our professor. Other than that, I have yet to learn anything really new…
• Honors Math: Essentially calculus with linear algebra, but from an analysis point of view. This class is definitely my hardest class – (proof-based) math is hard. Thankfully we just finished single-variable calculus and moved on to linear algebra, which is pretty intuitive.
• Ordinary Differential Equations: Tedium. Not to mention that I already knew most of the stuff. We’re getting to the interesting stuff like systems, etc. but I’m regretting signing up for this class. I recommend that physics major just pick up ODEs while doing other physics. Taking a class on it is pretty meh.
• Masterpieces of Western Literature: This is a pretty interesting (required core) class where we read and analyze works that have essentially transformed Western society into what it is today. So far – halfway into the semester – we’ve read: the Iliad, the Odyssey, the Hymn to Demeter, the three parts of Aeschylus’ Oresteia, Sophocles’ Oedipus Rex, Euripides’ Medea, and excerpts from Herodotus’ Histories and Thucydides’ History of the Peloponnesian War. I’d say this is my second-hardest class (after Honors Math)
• Frontiers of Science: To sum it up in a sentence… this is a required core class that is designed for non-science majors (but required for ALL students) that promises not to be an exercise in memorization and yet somehow manages to be nothing but that.

Aside from classes, I’ve met a bunch of really cool, really smart people. In fact, I’ll be participating in the University Physics Competition later today with two of the smartest freshman I’ve met… 48 hours of physics, here we come!

As for extracurriculars, I’m not doing much at this point. I wanted to do badminton and martial arts, but I only got my badminton racket from home, and I’ve been too lazy to decide whether to continue karate or to try something new. I am doing something interesting though – I’m working with a sophomore, Ariq Azad (who, I must admit, is doing most of the heavy-lifting), to develop a Columbia mobile app. We’ve just started, but it’s pretty fun so far! We hope to start releasing alpha versions sometime soon (we planned to work/release today but I realized the physics competition starts tonight and not on Saturday).

Anyway, I should go stock up on food and the like for during the competition, so I guess I’ll end my post here. By the way, I’ll probably post the paper we have by the end of the competition, Sunday evening-ish.

But oh, one last thing – I’ve gone back to using Windows recently (because Ubuntu has somehow halved my battery life and because I don’t like Unity) so I cleaned it up a bit, installed Rainmeter, and voila:

My desktop is orders of magnitude nicer than before