Two dimensions Definition and 139 Threads

Let ##a, b##, and ##c## be real numbers such that ##a## and ##c## are positive and ##ac > b^2##. Evaluate the double integral $$\int_{-\infty}^\infty \int_{-\infty}^\infty e^{-ax^2 - 2bxy - cy^2}\, dx\, dy$$

Some BSM theories, often but not exclusively string theory inspired, have an extra time dimension, as well as extra spatial dimensions. I'm trying to make sense of what it even means to have more than one time dimension, ideally, with a concrete example that illustrates how the second time...

But it seems to get too complex and am not sure whether it is correct.. my solution got a bit messy + incorrect Thanks in advance!

Hello everyone. I am working with mathematica, where I have developed a two-dimensional shannon interplation, just as can be seen in the slides 15 to 18 of this presentation. The code is as follows: savedX = Table[XposX = mat[[All, 1]]; YposX = mat[[All, 2]]; windXVal = mat[[All, i]]...

I stuck on part c and d. My attemption is attached.

For a single particle, $$Z=\frac{1}{h^2}\int_{-\infty}^{\infty} e^{-\beta \frac{P^2}{2m}}d^2p \int e^{-U(r)}drd\theta= \frac{1}{h^2}(\frac{2\pi m}{\beta}) 2\pi [\int_{0}^{r_0}e^{U_0}dr+\int_{r_0}^{R}dr]$$ $$ =\frac{1}{h^2}(\frac{2\pi m}{\beta}) 2\pi [e^{U_0}(r_0)+(R-r_0)]=\frac{\pi...

Since we don't know how far does it move in y-axis, I assumed that only x-component does work. a) W=Fx*Δx = 50N*(-6m) = -300 J b) Θ = arctan(12/50) = 13.5° But, I'm not sure that did I do this in right way...h

I don't know how to combine the x,y components with the equation of work.

I am creating a two-dimensional model of an ideal gas, and I was wondering how I should determine initial velocity. Ideally, I would like for the simulation to reach a point where the velocity distribution resembles that of the maxwell-boltzmann curve — will this be achieved if I, say, assign...

So imagine there are now two dimensions of time, instead of the one dimension which we're used to. The laws of physics which we're used to won't make anymore sense unless they're adapted for the two dimensions of time. How would you adapt them?

I attached an image with problem and the associated illustration. I don't know what the relevant equations are for this problem. Each and every time I read the problem I keep drawing a right triangle to represent the velocity components. The problem says the river is flowing east at 5km/h. I...

Homework Statement A bomb initially at rest is exploded into three pieces on a smooth, horizontal surface. Two pieces fly off at a 60° angle to each other, a 2.0 kg piece at 20 m/s and a 3.0 kg piece at 12 m/s. The third piece flies off at 30 m/s with an unknown direction. Determine the...

Homework Statement I am looking for references for the scalar field theory in one-space, one-time dimension defined by: $$\mathcal{L}=-\frac{1}{2}(\partial_{\mu}\phi)^2-\frac{1}{2}m_{2,0}^2\phi^2-\frac{1}{4!}m_{4,0}^2\phi^4-\frac{1}{6!}m_{6,0}^2\phi^6$$ That explains why the only divergences...

I and my teacher argued whether a uniform circular motion in polar coordinates is considered to be a motion in one dimension or it's a motion in two dimensions.

Homework Statement In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with a 0.40 kg puck B, which is initially at rest. Puck A moves at 4.2 m/s [W 30 N] . Find the final velocity of puck B. Homework Equations Conservation of momentum Pythagorean theorum The...

Homework Statement A ball of mass m hits the floor with a speed v making an angle of incidence theta with the normal. The coefficient of restitution is e. Find the speed of the reflected ball and the angle of reflection of the ball. The Attempt at a Solution I know that momentum is conserved...

Homework Statement Sorry for another question so soon, I am not sure if there is a limit on how many I can ask. I try to keep it to a minimum but sometimes I can't figure it out on my own. Question: In a physics lab, 0.30 kg puck A, moving at 5.0 m/s [W], undergoes a collision with 0.40 kg...

Homework Statement [/B]A 2.0 kg ball moving with a speed of 3.0 m/s hits, elastically, an identical stationary ball as shown (The first ball is traveling to the right). If the first ball moves away with angle 30° to the original path, determine the speed of the first ball after the collision...

Homework Statement Three charges, q1, q2, and q3, lie in a plane, as shown below. Find the net force on charge q2 (please refer to attachment for diagram) Homework Equations F= k x q1q2/R^2, knowledge of trig functions and separating x and y components The Attempt at a Solution So I found the...

I am trying to evaluate the following integral. ##\displaystyle{\int_{-\infty}^{\infty}f(x,y)\ \exp(-(x^{2}+y^{2})/2\alpha)}\ dx\ dy=1## How do you do the integral above?

Homework Statement Homework Equations xf = x0 + v0cos(θ)t + (1/2)axt2 yf = y0 + v0sinθt - (1/2)gt2 F = ma The Attempt at a Solution [/B] I first tried to find the acceleration in the x direction so I could solve for the force xf = x0 + v0cos(θ)t + (1/2)axt2 In order to find the time I used...

Im not sure where to find a good place to learn kinematics in one and two dimensions. Using calculus

Homework Statement A plane flies 600km/h south. The plane encounters a southwestern wind of 100km/h. Homework Equations What is the velocity (magnitude and direction) of the plane The Attempt at a Solution What I did was break the 100km southwestern vector into its components. 100*cos45 =...

I am a programmer trying to simulate some 2D balls bouncing about and colliding with each other. I have both the ball's velocity components before the collision and I am trying to solve for them. I went to wikipedia to find a formula to satisfy my needs and ran into this section...

Homework Statement Homework Equations ∫F⋅dr=W The Attempt at a Solution

Hi, Gleason's theorem fails if the dimension of the Hilbert space is two. Does this allow for violations of Born's rule in two-dimensional systems? Or can you somehow tensor the system with the (ever-present and infinite-dimensional) Hilbert space of the rest of the universe, apply Gleason's...

1. Homework Statement (The following is taken from Sears and Zemansky’s University physics with modern physics, thirteenth edition by Young Freedman. Chapter 3 bridging problem: Launching up an incline at page 95. You fire a ball with an initial speed ##v_0## at an angle Φ above the surface...

Homework Statement hello guys, that's the problem, when i tried to solve it using soh cah toh and Pythagoras law it resulted in answers e' and f', which make sense to me because both result it 54.6N and both relevant in directions so i am a bit confused.[/B] Suppose that a force with a...

Homework Statement A baseball weighing 140g is traveling to the right at 35 m/s, makes contact with a baseball bat, and then leaves the bat at 55 m/s to the left at an angle 25 degrees from the horizontal. I got the right answer, I how how the solution works mathematically. The answer is...

Question: In an anniversary celebration of Marilyn Bell's 1954 feat- she was the first person to swim across Lake Ontario- a swimmer set out from the shores of New York and maintained a velocity of 4m/s (N). As the swimmer approached the Ontario shore, she encountered a cross-current of 2 m/s...

Homework Statement I need to find velocity v from the drawing. Homework Equations Equations of kinematics The Attempt at a Solution I found that v=12.134 m/s . I need to know is it correct. [/B]

Homework Statement a boy on whom the force of gravity is 400 N hangs on to the middle of a rope stretched between two trees. The rope sags in such a way that it makes an angle of 170 degrees at the boys hands. what force does the rope exert on each tree? Homework Equations F=ma The Attempt at...

Homework Statement The problem is stated here (from brilliant.org) http://i.imgur.com/MkWwnjT.png Homework Equations momentum = mass * velocityThe Attempt at a Solution My attempt at a solution can be found here: http://i.imgur.com/Zsco86W.jpg I get the answer 0.035kg, but that is not an...

Homework Statement A soccer ball is kicked from the ground at an angle of 30◦ with speed 30m/s. Determine the duration of the flight, range and maximal height of the trajectory. Homework EquationsThe Attempt at a Solution 1. Break down the velocity vector into x and y components: 30cos(30) =...

Homework Statement A freight train is moving at a constant speed of 10 m/s. A man standing on a flatcar throws a ball into the air and catches it as it falls. Relative to the flatcar, the initial vellocity of the ball is 15 m/s straight up. a. What are the magnitude and direction of the...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] A balloon going upwards with a velocity of 12 m/s, is at a height of 65m from the Earth at any instant. Exactly at this instant a packet drops from it. How much time will the packet take...

Motion in two dimensions! Help! Homework Statement The coordinates of an object moving in the xy plane vary with time according to the equations x =-5.00 sin (vt) and y= 4.00 - 5.00 cos (vt), where v is a constant, x and y are in meters, and t is in seconds. (a) Determine the components...

Homework Statement Two thin rods are fastened to the inside of a circular ring as shown in the figure below. One rod of length D is vertical, and the other of length L makes an angle θ with the horizontal. The two rods and the ring lie in a vertical plane. Two small beads are free to slide...

Homework Statement Two tugboats are pulling a large log, as shown in the following diagram. The log has a mass of 250 kg and is initially at rest. How far have the tugboats moved the log after 10 s? http://imgur.com/GS7Y80x Homework Equations c^2=a^2 + b^2 -2ab cosC sin A/ a= sin...

Homework Statement A bird flies from Lesser Slave Lake in northern Alberta to Dore Lake in northern Saskatchewan. The birds displacement is 800.0 km [E 7.5deg S]. The bird then flies from Dore Lake to Big Quill Lake, Saskatchewan. This displacement is 400.0 km [E 51deg S]. The total time of...

Homework Statement During baseball practice, you go up into the bleachers to retrieve a ball. You throw the ball back into the playing field at an angle of 42° above the horizontal, giving it an initial velocity of 15 m/s. If the ball is 5.3 m above the level of the playing field when you...

In an experiment, one of the forces exerted on a proton is F = −αx^2i , where α = 14.4 N/m2. (a) How much work does F do when the proton moves along the straight-line path from the point (0.10 m, 0) to the point (0.10 m, 0.5 m)? (b) Along the straight-line path from the point (0.09 m, 0) to...

Hi all, Had a doubt regarding Laplace's equation. In many textbooks, the general solution to the two dimensional Laplace's equation is mentioned as: \Phi(\rho,\phi) = A_{0} + B_{0}ln(\rho) + \sum_{n=1}^{\infty}\rho^n(A_ncos(n\phi) + B_n sin(n\phi)) + \sum_{n=1}^{\infty}\rho^{-n}(C_n cos(n\phi)...

Problem: A hockey puck rebounds from a board as shown in figure 16. The puck is in contact with the board for 2.5 ms. Determine the average acceleration of the puck over the interval. t = 0.0025 s |vi|= 26 m/s |vf| = 21 m/s aav = ? *v and a are vectors* I have made several attempts to...

Homework Statement Let f : ℝ2 -> ℝ be some function that is defined on a neighborhood of a point c in ℝ2. If D1f (the derivative of f in the direction of e1) exists and is continuous on a neighborhood of c, and D2f exists at c, prove that f is differentiable at c. Homework Equations...

A worker works in a roof and let's a hammer fall over the roof with the speed 4m/s.The roof forms an angle 30 degree related to the horizon and its lowest point its 10meters from the ground.What is the horizontal displacement of the hammer from the moment he leaves the roof to the moment he...

1. On a table (defining the x,y-plane laying 3 identical coins A,B and C with identical diameter of 18.00mm. The coordinates of their centers are Z(0,0), Y(60.0,0), X(60.0, 45.0) all given in mm. Under what angle relative to the x-axis one has to push Z against Y so that Z performs after the...

Homework Statement Fast Eddie McSpeedy is a receiver for the Kennesaw Kilowatts in the Metro Metric Football League and Big Bobby Clobber plays defense in the rival Marietta Megatons. Eddie has a mass of 85 kg and Bobby has a mass of 140 kg. Eddie catches the ball and runs eastward at 2.4 m/s...

Homework Statement A car initially traveling due north goes around a semicircle having a radius of 500 m at a constant speed of 20 m/s. A) How long does this take? B) What is the magnitiude and direction of the average acceleration? Homework Equations a = Δvx/Δt(xhat)+Δvy/Δt(yhat)...