2d Definition and 1000 Threads

Say I have a rectangle of width w and height h centred at (0, 0) on a 2D coordinate plane. The rectangle is free to move on a frictionless medium. It is not attached at any point. Case 1: A single force F = (Fx)i + (Fx)j acts at a point (x, y) How does the rectangle move? I looked it up on...

This is a problem that's appeared in a game I am writing, and is a bit beyond the mechanics I can sort-of remember from high school. The context is I have an object in 2D space which has a position p and a velocity u, and a goal position G I want that object to be in as soon as possible. At...

How to do integration for a 2D matrix using MATLAB? That is to say, suppose I have a bunch of data points over a rectangular region in xy plane, how to find the integral over this plane? More explicitly, suppose I want to integrate over a square region, [0,4]x[0,4] my data is 2 4 5...

Homework Statement So, I'm building a "Monkey Gun" and I want to be able to find the instantaneous velocity of my dart at a certain time. I shoot the gun at some angle, θ. The problem is, if I divide the velocity into x and y components, each depends on and impacts the other (the force from...

Homework Statement Consider metric ds2 = dx2 + x3 dy2 for 2D space. Calculate all non-zero christoffel symbols of metric. Homework Equations \Gammajik = \partialei / \partial xk \times ej The Attempt at a Solution Christoffel symbols, by definition, takes the partial of each...

A soccer player kicks a rock horizontally off a cliff 38.2m high into a pool of water. If the player hears the sound of the splash 3.13s later, what was the initial speed given to the rock? Assume the speed of sound in air to be 343m/s What I don't understand here is, determining the...

I'm looking for an analytical solution to a very simple problem I've come across. Start with a circle of radius a. Now place n points at random positions inside this circle. Can you calculate the expectation value for the mean distance between the points? For the sake of argument can you...

Homework Statement I am having trouble understanding how the following statement (taken from some old notes) is true: >For a 2 dimensional space such that ds^2=\frac{1}{u^2}(-du^2+dv^2) the timelike geodesics are given by u^2=v^2+av+b where a,b are constants. Homework Equations...

Homework Statement A person moving towards east with a speed 'v' observes the rain to be falling vertically downwards. When he doubles his speed, the rain appears to come at 30° angle with the vertical. Find the actual speed and direction of rain with vertical. Homework Equations...

Why is a single layer of atoms referred to as "2d"? I commonly hear a single layer of atoms referred to as being a "2-dimensional structure", when it so clearly is not 2-dimensional. Why do people make that obvious mistake? The same exact folks will also tell you that spacetime is a...

Hi I have this small doubt. i am not good in C . i like to bring i,j,pi values to subroutine and bring back Asi to main program. how to write ! Plz help.. #include <stdlib.h> #include <math.h> double A_operate(int i,int j) void main() { double Ai, pi[10][10],r[10][10]; int i,j,n,m; n=6...

Homework Statement A two-dimensional rectangular crystal has a unit cell with sides a 6.28Å and b 3.14Å. A beam of monochromatic neutrons of wavelength 5.0 Å is used to examine the crystal. Using either the Laue condition for diffraction or Bragg's Law, determine whether it would be...

Homework Statement In a game of billiards the 0.165 kg cue ball is hit toward the 0.155 kg eight ball which is stationary. The cue ball travels at a speed of 6.2 m/s and after impact rolls away at an angle of 40.0 degrees counterclockwise from its initial direction with a velocity of 3.7 m/s...

Hey everybody I've got a question for the programming savvy. I'm generating data which can generally be described by.. f(x,y) = Ʃn(an * xn)*Ʃn(bn * yn) Basically what I'm looking at is a data set which shows a surface which looks like about 1/4th of a wonky bowl. My trouble is...

When I was about 25 I noticed that a 2D photo appeared 3D when looked at through a magnifying glass. First I thought it depended on the lens, but then realized it was because I looked at the picture by just one eye - exactly as the camera lens had seen it in reality. I.e. there is much 3D...

Hello science folks! I've just started learning about trilateration. I am wondering if its possible to calculate the coordinates of a continuously growing circle(for example a sound wave) which hits three sensors at different times. I have added a picture so you can see what I mean. In the...

Hi, I'm trying to adapt the doppler shift formula for a stationary listener and a source traveling in a straight line towards/away from the listener to the case where the source does not move straight towards the listener. For example, suppose that I am looking north and train further in the...

Hello, for the Poisson problem Δu = -1 on a 2D circular disk with u = 0 on the boundary, we have average(u) = \frac{1}{8\pi}Area(disk), which is easy to see, as the solution is quadratic in the polar coordinate r. Does this (or a similar) relation hold for non-circular 2D domains? This...

Homework Statement A ball is kicked with initial velocity 40 m/s at an angle of 37 degree above the horizontal. What is the time (in seconds) needed to reach the maximum height? Homework Equations Y-axis h= Voy t - 0.5 g t^2 Vy= Voy - g t Vy^2= Voy^2 - 2 g h X-axis d= Vox t Vx=...

I'm currently working on a project for a code that does umbrella sampling of a 2-D Ising model [size LxL of a magnet (analyzing up or down spins)]. The next step is to take my code to analyze a nucleation region and its growth by varying the temperature above critical. Before I even attempt to...

Homework Statement We have this bridge, which is 2D - as shown picture. How I determine which sticks are subjected to pressure and which tension? How big are these forces? Sticks are intangible, mass of car is M. From the picture, we can determine the length of the sticks. Picture...

1. a 52 Kg mountain climber is suspended from a cliff by a rope. Given a few bits of information the angle formed by the rope to the climber is 31 degrees The angle of the climbers legs is 15 degrees north of horizontal (a) Find the tension in the rope and the force that the mountain...

So the way we learned to solve elastic collisions is to use the center of mass reference frame. I calculated that the COM is moving at v=1.66 m/s relative to the lab frame. Next I calculated the velocity of the white ball to be +1.66 m/s relative to the COM frame and the black ball to have...

Homework Statement A Projectile is launched from the top of a 100m tower and falls 20m below the bottom of the tower and 90m away in the x direction. Time of flight is 6 seconds. 1. Find the x component of the velocity of the object when it strikes the ground. 2. Find the y-component of...

Homework Statement " An airplane turns slowly for 9.2s horizontally. The final velocity of the plane is 360km/hr [N]; the average acceleration during the turn is 5.0m/s^2 [W]. What is the initial velocity of the plane?" Homework Equations a=ΔV/t The Attempt at a Solution at=Δv...

1. The Ferris wheel [...] rotates counterclockwise, is just starting up. At a given instant, a passenger on the rim of the wheel and passing through the lowest point of his circular motion is moving at 3.00 m/s and is gaining speed at a rate of 0.500 m/s^2 . 2. Find the direction of the...

I am designing a 2D model of a three-phase core-type transformer in ANSOFT MAXWELL 14.0. While doing so I have encountered a strange problem. Start of the problem:- While designing the transformer, I wanted to incorporate core losses. So, I did the following steps:- Excitations -> Set...

I am designing a 2D model of a three-phase core-type transformer in ANSOFT MAXWELL 14.0. While doing so I have encountered a strange problem. Start of the problem:- While designing the transformer, I wanted to incorporate core losses. So, I did the following steps:- Excitations -> Set...

Homework Statement A 0.30 kg puck A, initially at rest on a frictionless horizontal surface, is struck by a 0.20 kg puck B that is initially moving along the x-axis with a velocity of 2.0 m/s. After the collision, the 0.20 kg puck has a speed of 1.0 m/s at an angle of θ = 530 to the positive...

Hello. I'm new on this forum and I hope I'm posting this in the right place. This is not for a homework assignment but a spare-time project I'm working on. Homework Statement The goal with this project is to make a simple program that simulates an object that orbits a single fixed point...

I am stuck on the following task; Create a 2D Parametric Plot showing a spiral path. The parametric equations for a logarithmic spiral are x=k^u Cosine(u), y=k^u Sine(u), where k is a constant, and u is the plot parameter. What does the value of k determine? I have been typing in the...

Homework Statement Solve for the unit vectors x-hat and y-hat in terms of r-hat and phi-hat. Homework Equations r-hat=cos(phi)x-hat+sin(phi)y-hat phi-hat=cos(phi)y-hat-sin(phi)x-hat, The Attempt at a Solution I have been working on this for a really long time, and I keep getting a...

The figure shows the successive displacements of an aircraft flying a search pattern. The initial position of the aircraft is P and the final position is P'. What is the net displacement (magnitude and direction) between P and P'? My attempt: So, my understanding is that the net...

The integration by parts rule in two dimensions is \int_{Ω}\frac{\partial w}{\partial x_{i}} v dΩ = \int_{\Gamma} w v \vec{n} d\Gamma - \int_{Ω} w \frac{\partial v}{\partial x_{i}} dΩ I have two examples in polar coordinates In first example I have \vec{n}=\vec{n_{r}} \int_{\Gamma}...

Im trying to calculate the refelction angle of 2 points in a 2d plane, but not the same distance away from the reflection surface, and I'm drawing a blank. Any help would be hugely appreciated.

The combination of special relativity and quantum mechanics in a single framework makes our understanding of such systems to be true only in 4D, Minkowski space...I have noticed that recent published work concerning 2D systems and I am not sure about this reduction of 4D to only 2D, does it mean...

The problem: (Note: the correct answer is bolded throughout) A basketball is launched with an initial speed of 8 m/s at a 45 degree angle from the horizontal. The ball enters the basket in 0.96 seconds. What is the distance x and y? Just ignore the distance x, I know it's simply the product...

Integral through a path in 2D (or ND) What's the usual "definition"? [Bold letters are vectors. eg: r] We have a scalar function f(r) and a path g(x)=y. I see two ways to reason: (1) The little infinitesimals are summed with the change of x and on the change of y separately. (2) The little...

Homework Statement Say we have a 2D rigid body transform, with parameters p = [ p_1,p_2,p_3] for rotation, x translation and y translation respectively. I'm using the transform to .. transform an image. Is there a way to have: For a point x , y : x',y' = transform(x,y,p) <=> x,y =...

Hello Everyone, I am having a heck of a time with collisions in 2D and with rotational kinetics and rotational dynamics. I have posted 5 questions below that I seem to be having the most troubles with. I know it my be a lot to ask but if anyone here can help me to understand how they got to...

I havn't had much classes on numerical methods in quantum mechanics and I'm wondering how one would solve a general problem involving 2d motion. With general, I mean a problem that cannot be separated. Consider for instance the hamiltonian \hat{H} =...

Hey everyone! I have the following question for you guys to settle an argument: If you were an inhabitant of Flatland and a cube decided to visit you like the sphere did, would you be able to see more than 2 sides at a time? My answer is no because Mr. Cube could appear as a point, a square...

Hi everyone! Let me introduce myself, my name is Francisco and I'm an architecture student. I've recently become interested in algorithmic design, which is basically utilizing math to help design (an example would be structure or space optimization). To contextualize, I am a noob with...

Homework Statement A cannon is fired at an angle of 42 degrees, the cannon ball travels 8.9 meters in the x direction. Its hang time is 1.5 seconds. The cannon site .43 meters above the ground on a stand. If this same cannon was fired at 35 degrees, what would the hang time and the distance...

Hello, If a rotation of a 2-d disk about a 1-d line can produce centrifugal gravity, is it right to infer that rotation of a 3-d volume about a 2-d plane would create gravity, observable in the 3-d volume? It is confusing to think about the direction of this gravity, if it exists...

Hi all, If I have a Gaussian with the equation: G(x,y) = h*exp(-(x-x0)^2/a -(y-y0)^2/b) where x0, y0, a, b and h are the parameters which may vary, what's the equation for the elliptical contour line at the half-max of G? I'm getting myself confused! Thanks for help

Hello, I consider two functions f:R^2 \rightarrow R and g:R^2 \rightarrow R, and the two dimensional convolution (f \ast g)(\mathbf{x}) = \int_{\mathbb{R}^2}f(\mathbf{t})g(\mathbf{x-t})d^2\mathbf{t} I proved using the Fourier transform and the convolution theorem that the convolution of two...

Any python/matplotlib experts out there?? This one has been driving me crazy all day. I have three vectors, azimuth, frequency and power, which I would like to histogram and plot on a polar axis. I can plot a scatter plot this way no problem but the histogram gets messed up somehow. An example...

Hi all! I would like to extrude a 2d curve in the X-Y plane along the Z direction,thereby wanting to obtain a plane of Z units long.How should I proceed? Is there a tool especially for this in MATLAB?

Homework Statement Andy (mass 92 kg) and Sam (mass 75 kg) are both on toboggans (each toboggan has a mass of 4.6 kg) traveling on a crash course towards each other. Just as they hit, they lock hands so they move together as one. What is their new speed? In what direction do they travel? mA =...