What is Two dimensions: Definition and 143 Discussions

Two-dimensional space (also known as 2D space, 2-space, or bi-dimensional space) is a geometric setting in which two values (called parameters) are required to determine the position of an element (i.e., point). The set ℝ2 of pairs of real numbers with appropriate structure often serves as the canonical example of a two-dimensional Euclidean space. For a generalization of the concept, see dimension.
Two-dimensional space can be seen as a projection of the physical universe onto a plane. Usually, it is thought of as a Euclidean space and the two dimensions are called length and width.

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  1. V

    Acceleration in Two Dimensions

    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)...
  2. P

    Kinematics-acceleration in two dimensions

    Homework Statement A tennis player standing 8.0 meters from the net hits a ball 1.5 meters above the ground toward her opponent. The ball leaves her racquet with a speed of 25.0m/s at an angle of 14.0 degrees above the horizontal. The net is 1.0 meters high. The baseline is 12 meters back...
  3. bcrowell

    Exploring Torsion in 2 Dimensions: A Differential Geometry Perspective

    This is really more of a differential geometry question than a GR question. Is it possible to have torsion in two dimensions? I've seen statements implying that torsion is only of interest in 3 or more dimensions, but I don't see why. My understanding is that in two dimensions, you could not...
  4. A

    Wess Zumino model in two dimensions

    Homework Statement Hi! I need some help to describe a Wess Zumino model in two dimensions: spinors are real (because of the Majorana condition \theta=\theta^{\ast}) and have two components; the superfield is: \phi \left( x,\theta\right)=A\left( x\right) +...
  5. A

    Mass dimension of a scalar field in two dimensions?

    Which is the mass dimension of a scalar filed in 2 dimensions? In 4 dim I know that a scalar field has mass dimension 1, by imposing that the action has dim 0: S=\int d^4 x \partial_{\mu} A \partial^{\mu} A where \left[S\right]=0 \left[d^4 x \right] =-4 \left[ \partial_{\mu} \right]=1...
  6. Math Amateur

    Finite Reflection Groups in Two Dimensions - R2

    I am seeking to understand reflection groups and am reading Grove and Benson: Finite Reflection Groups On page 6 (see attachment - pages 5 -6 Grove and Benson) we find the following statement: "It is easy to verify (Exercise 2.1) that the vector x_1 = (cos \ \theta /2, sin \ \theta /2 )...
  7. M

    Momentum collision in two dimensions

    Homework Statement A light passenger vehicle weighing 1470 N collides with a train engine weighing 1.23 x 10^5 N, which was being moved from one rail siding to another. The train engine and the vehicle were entangled after the accident and from your measurements you have been able to...
  8. J

    Inelastic collisions in two dimensions

    A light passenger vehicle weighing 1470 N collides with a train engine weighing 1.23 x 105 N, which was being moved from one rail siding to another. The train engine and the vehicle were entangled after the accident and from your measurements you have been able to determine they skidded 15 m...
  9. O

    What is the direction of the neutron's velocity after the collision?

    Homework Statement A neutron (mass 1.7x10-27 kg) traveling at 2.7 km/s hits a stationary lithium nucleus (mass 1.2x10-26 kg). Afterwards, the velocity of the lithium nucleus is 0.40 km/s at 54° to the original direction of the motion of the neutron. If the speed of the neutron after the...
  10. B

    Kinematics In Two Dimensions - Archery

    Homework Statement Hey guys, so here's the problem I'm given: You are watching an archery tournament when you start wondering how fast an arrow is shot from the bow. Remembering your physics, you ask one of the archers to shoot an arrow parallel to the ground. You find the arrow stuck in the...
  11. C

    Acceleration in Two Dimensions of watercraft

    Homework Statement A watercraft with an initial velocity of 6.4 m/s [E] undergoes an average acceleration of 2.0 m/s2 [S] for 2.5 s. What is the final velocity of the watercraft?Homework Equations vf = vi + a * t a = v / t v = v2 + (-v1) pythagoras and cosine law? The Attempt at a Solution I...
  12. L

    Special relativity assignment - pole moving in two dimensions

    Hi! I'm a bit stuck with this special relativity assignment, here's is the problem: So the problem here is that not only does the hole shrink in S', as stated in the problem description, the pole should also be wider by a factor of 3 in this frame. So we have an 18 ft wide pole that has to...
  13. J

    Inelastic Collision in Two Dimensions

    Homework Statement A 1300-kg car collides with a 15,000-kg truck at an intersection and they couple together and move off as one leaving a skid mark 5m long that makes an angle of 30.0° with the original direction of the car. If μk = 0.700, find the initial velocities of the car and truck...
  14. T

    Statics of body in two dimensions

    Homework Statement Homework Equations A 50 lb force is applied to a corner plate as shown. Determine an equivalent system consisting of a 150 lb force at B and another force at A. The Attempt at a Solution There is an algebraic solution to the problem, but I was wondering if it...
  15. M

    Kinematics in two dimensions lab question

    Homework Statement Using your understanding of projectile motion along with some background research on video analysis, devise a way to find the initial velocity of the tennis ball in the video just as it enters the bottom left of the screen. There is some important information for you to...
  16. A

    Maximum Initial Velocity of a Tennis Ball: Solving for the Optimal Launch Speed

    Hi there all, I'm new to this forum and I really need some help. The question is described as follows: Estimate the maximum "initial velocity" that you can achieve with a regular tennis ball. Presumably there are no variables, nor are there any equations involved. I think that an...
  17. F

    Relative motion in two dimensions question

    Ship A is located at 4 km north and 2.5 km east of ship B. Ship A has a velocity of 22 km/h toward the south, and ship B has a velocity of 40 km/h in a direction 37 degrees north of east. (a) What is the velocity of A relative to B in unit-vector notation with i toward the east? (b) Write an...
  18. S

    Bravais Lattice in Two Dimensions

    In the book Applied Physics by P.K.Mittal, on page#25 under the heading of "Bravais lattice in two dimensions", a paragraph says, "The number of point groups in two dimensions is 10." My 1st question is, Then how many in three dimensions? Paragraph further says, "10 groups in two...
  19. F

    What is the relationship between horizontal and vertical radii in a bent pipe?

    I have a question, and I hope I can word it correctly. Say I have a round pipe of length 5 feet (actually, the length is irrelevant). I want to bend it at a certain radius in the horizontal direction, and also a certain radius in the vertical direction. Let's say I bend it at 20' horizontal...
  20. Loren Booda

    3-body solution in two dimensions

    Are there any exact solutions for two-dimensional projections of 3-body problems?
  21. G

    A Momentum-collision problem two dimensions (HELP)

    Homework Statement An m = 6.20-kg clay ball is thrown directly against a perpendicular brick wall at a velocity of 22.0 m/s and shatters into three pieces, which all fly backward, as shown in the figure. The wall exerts a force on the ball of 2660 N for 0.110 s. One piece of mass m1 = 2.20 kg...
  22. Q

    Proving differentiability in two dimensions

    Homework Statement proof at 0,0 g(x,y) is differentiable Homework Equations notes says i have to write in the form fx(0,0)\Deltax + fy(0,0)\Deltay + E1\Deltax + E2\DeltayThe Attempt at a Solution i compute fx(0,0) = 0 and fy(0,0) = 0 but what's the E talking about? what am i trying to do...
  23. V

    Movement in one and two dimensions, where finding Force in a problem

    Homework Statement Hello everyone, i have been stuck on this question on the Physics year 12 Nelsons textbook, and it is pissing me off because I've been working so hard on it and i can not get it. It is in the chapter of Movement in one and two dimensions. The question is: A person...
  24. S

    Relativistic Trains in Two Dimensions

    Homework Statement A and B are trains on perpendicular tracks, radiating from the origin of a coordinate system S. Train A is moving along the positive Y axis at a velocity of 0.8c, and train B is moving along the positive X axis also at a velocity of 0.8c. All velocites are measures with...
  25. K

    Motion in two dimensions

    Homework Statement An object moves clockwise with decreasing speed around an oval track. There are velocity vectors at two points (G and H). G has a greater speed than H. Is the angle between the acceleration and velocity vector of G greater than, less than, or equal to 90 degrees...
  26. D

    Gr. 12 - Conservation of Momentum in Two Dimensions

    Homework Statement This question is from a correspondence course I'm taking: Two spacecraft from different nations have linked in space and are coasting with their engines off, heading directly toward Mars. The spacecraft s are thrust apart by large springs. Spacecraft 1, with a mass of...
  27. K

    Stability of a spring mass system in two dimensions

    Homework Statement Attached Homework Equations 5.104 mentioned in the problem is Also attached The Attempt at a Solution Suppose the mass is moved to (x,y), the distance from the mass to the left spring is denoted by A, the distance from the mass to the right spring is denoted...
  28. P

    Motion in two dimensions basketball dunk

    Homework Statement A basketball star covers 2.40 m horizontally in a jump to dunk the ball (see figure). His motion through space can be modeled precisely as that of a particle at his center of mass. His center of mass is at elevation 1.02 m when he leaves the floor. It reaches a maximum...
  29. B

    Problem with relative motion in two dimensions

    Homework Statement Ship A is located 4.8 km north and 3.0 km east of ship B. Ship A has a velocity of 22 km/h toward the south and ship B has a velocity of 40 km/h in a direction 37° north of east. (a) What is the velocity of A relative to B (Express your answer in terms of the unit vectors i...
  30. M

    How Do You Calculate the Explosion Coordinates of an Artillery Shell?

    Homework Statement An artillery shell is fired with initial velocity of 300 m/s at 55 degrees above the horizontal. TO clear an avalanche, it explodes on a mountainside 42 secs after firing. What are the x- and y- coordinates of the shell where it explodes, relative to its firing point...
  31. R

    Calculating Recoil Momentum in Two-Dimensional Nuclear Decay

    Homework Statement A radioactive nucleus at rest decays into a second nucleus, an electron and a neutrino.The electron and neutrino are emitted at right angles and have momenta of 9.3x10^23kg*m/s and 5.40x10^23kg*m/s, respectively. What are the magnitude and direction of the momentum of the...
  32. R

    How Do You Determine the Velocity and Angle of a Billiard Ball After Collision?

    Homework Statement Billiard ball A of mass mA= 0.400kg moving with speed vA=1.80m/s strikes ball B initially at erst, of mass mB=0.500kg.As a result of the collision,ball A is deflected off at an angle of 30.0degrees with a speed v'A=1.10m/s. Taking the x-axis as the original direction of...
  33. M

    Finding the Net Force in Two-Dimensional Motion

    Homework Statement Three students push a box. Michael pushes with a force of 200 N at 0 degree. Shannon exerts a force of 150 N at 30 degrees, and Adam pushes with 175 N at 145 degrees. What is the magnitude of the net force? Homework Equations Some trig nothing special The Attempt...
  34. A

    Momentum: Glancing collisions in two dimensions

    Homework Statement a ball of mass 2kg is traveling North with a Velocity 6m/s when it collides with an identical, stationary ball. after the collision, one of the ball moves with a velocity of 2m/s at an angle of 30deg east of north. find Velocity of the other ball. m1=2kg m2=m1 v1=6m/s...
  35. K

    Motion in Two Dimensions of darts

    Homework Statement In the game of darts, the player stands with feet behind a line 2.36 m from a dartboard, with the bull's-eye at eye level. Suppose you lean across the line, release a dart at eye level 2.23 m from the board, and hit the bull's-eye. Find the initial velocity of the dart, if...
  36. E

    How Fast Were the Spacecrafts Traveling Before Separation?

    Homework Statement Two spacecraft from different nations have linked in space and are coasting with their engines off, heading directly toward Mars. The spacecraft s are thrust apart by large springs. Spacecraft 1, with a mass of 1.9 x 10^4 kg, then has a velocity of 3.5 x 10^3 km/h at 5.1...
  37. K

    Work Done in Two-Dimensional Ramp Push

    Homework Statement A worker pushed the Piano weighing 93N up a ramp into a moving van, pushing horizontally, parallel to the ground. The ramp extends 4m over the ground and 3m high. The top, sloped surface of the ramp holding the piano is 5m long. The worker exerts a force of 85 N. How much...
  38. A

    How Can I Master Kinematics in Two Dimensions?

    Having diffuclty understanding the concepts, etc. I did alright for one dimension, but now I am pretty lost. I have trouble knowing what to find and how to draw everything out. (Chapter 3, Cutnell & Johnson, 7th Edition). Does anyone have any recommendations on online outlines or even youtube...
  39. W

    What were the velocity and direction of the glass as it fell?

    A glass is slid across a table top, goes off the edge and falls to the floor. The table is 0.860m high and the glass lands 1.53m from the edge. a)With what velocity did the glass leave the table top? b)What was the direction of the glass's velocity(degrees clockwise from the horizontal)as it...
  40. M

    Questions in [ motion in two dimensions ]

    questions in [ motion in two dimensions ] q. [ .. if you know the position vectors of a particle at two points along its path and also know the time interval during which it moved from one point to the other m can you determine the particle's instananeous velocity ? its average velocity ...
  41. 6

    Solving Schrodinger equation in two dimensions

    Homework Statement Solve the time independent Schrodinger equation for an electron in a 2-D potential well having dimensions Lx and Ly in the x and y directions respectively.Homework Equations d^2Y/dx^2 + d^2Y/dy^2 + 2m/h^2*EY = 0The Attempt at a Solution Y(x) = A exp(jkx) + B exp(-jkx) I'm...
  42. D

    Kinematics in two dimensions problem

    A fire fighter directs a stream of water from a fire hose into the window of a burning building. The window is 20.0 m above the level of the nozzle and 60.0 m away. The hose produces a jet of water at a constant nozzle speed of v0 = 30.0 m/s. The fire fighter can control the angle θ0 that the...
  43. P

    Euqation of kinematics in two dimensions

    Fans claim that Michael Jordan is able to jump and remain in the air for two full seconds from launch to landing. Evaluate this claim by calculating the maxium height that such a jump would attain. For comaprsion, Jordan's maximum jump height has been estimate at about one meter. Y=1meter...
  44. P

    Euquations of kinematics in two dimensions

    A golfer imparts a speed fo 26.0m/s to a ball, and it travels the maximum possible distance before landing on the green. The tee and the green are at the same elevation. A.) How much time does the ball spend in the air? B.) What is the longest "Hole in one" that the golfer can make, if the ball...
  45. C

    Kinematics in two dimensions - question?

    I'm having problems with this problem. Can anyone help me? A space vehicle is coasting at a constant velocity of 21.4 m/s in the +y direction relative to a space station. The pilot of the vehicle fires a RCS (reaction control system) thruster, which causes it to accelerate at 0.350 m/s2 in...
  46. T

    What is the Original Speed of Linked Objects in Two Dimensions?

    Homework Statement Object 1: m1=1.9x10^4 kg v1'= 972 m/s [E5.1*N] Object 2: m2=1.7x10^4 kg v2'=944 m/s [E5.9*S] Determine their original speed when they were linked together. Homework Equations Pti = Ptf m1v1 + m2v2 = m1v1' + m2v2'
  47. S

    Collision in two dimensions (not heads on)

    Homework Statement Puck A has a mass of 0.0320 kg and is moving along the x-axis with a velocity of +7.65 m/s. It makes a collision with puck B, which has a mass of 0.0640 kg and is initially at rest. The collision is not head-on. After the collision, the two pucks fly apart with the angles 65...
  48. P

    How Fast Must a Quarterback Throw to Achieve a 171 Meter Pass?

    Homework Statement A quarterback claims that he can throw the football a horizontal distance of 171 m. Furthermore, he claims that he can do this by launching the ball at the relatively low angle of 26.2 ° above the horizontal. To evaluate this claim, determine the speed with which this...
  49. W

    How Does Tension Affect Motion on a Frictionless Surface?

    Homework Statement A box of mass M=10 kg is at rest on a frictionless level surface (like an ideally smooth ice rink). A rope tied to the box is pulled horizontally, such that the tension in the rope is T = 75 ˆx + 25 ˆz N, where both the x-axis and the z-axis are parallel to the floor. What...
  50. J

    Ideal gas law in two dimensions?

    Hi everyone, I know that in P=nRT/v R = 8.314 m3*Pa/mol*k Now, when you are trying to calculate P, if you have volumn in m3 on the bottom, everything cancels out and you are left with Pa. I've just developed a simulator which simulates particle motion over time and calculates...
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