# What is Two dimension motion: Definition and 13 Discussions

A two-dimensional gas is a collection of objects constrained to move in a planar or other two-dimensional space in a gaseous state. The objects can be: classical ideal gas elements such as rigid disks undergoing elastic collisions; elementary particles, or any ensemble of individual objects in physics which obeys laws of motion without binding interactions. The concept of a two-dimensional gas is used either because:

(a) the issue being studied actually takes place in two dimensions (as certain surface molecular phenomena); or,
(b) the two-dimensional form of the problem is more tractable than the analogous mathematically more complex three-dimensional problem.While physicists have studied simple two body interactions on a plane for centuries, the attention given to the two-dimensional gas (having many bodies in motion) is a 20th-century pursuit. Applications have led to better understanding of superconductivity, gas thermodynamics, certain solid state problems and several questions in quantum mechanics.

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1. ### Show that a projectile lands at a distance ##R = \frac{2v_0^2 sin \theta cos(\theta + \phi)}{g cos^2 \phi}##

##V_x = V_0 cos \theta ## ##x = V_0 cos \theta t## ##V_y = V_0 cos \theta ## ##y = V_0 cos \theta t## ##F_x = m\ddot{x}## ##-mgsin \phi = m\ddot{x}## ##\dot{x} = -gtsin\phi + V_x## ##x = -\frac{1}{2} gt^2 sin \phi + V_x t## ##x = -\frac{1}{2} gt^2 sin \phi + v_0 cos\theta t## ##F_y =...
2. ### Maximum Distance a Projectile Moves Up an Inclined Plane

the red line is the initial velocity, the grey parabola is the path of the projectile. hi there...I'm kinda stuck at the part b of this problem. I can do part a with no problem. can anybody explain to me how to do the differentiation needed to solve part b?? by explain I mean explain the...
3. ### I'm having a comprehension issue with a 2-D motion problem.

1. Problem Statement A 2 kilogram block rests at the edge of a platform that is 10 meters above level ground. The block is launched horizontally from the edge of the platform with an initial speed of 3 meters per second. Air resistance is negligible. The time it will take for the block to reach...
4. ### Difference between relative velocity and effective velocity

Can anyone tell me the difference between concept of relative velocity and effective velocity and when to use the concept of relative velocity? For example, if a guy throws a ball from a moving object at an angle theta it undergoes projectile motion we write horizontal velocity as...
5. E

### Projectile Motion: Determining Launch Angle

Homework Statement A hunter aims a high velocity semi-automatic rifle at a moose that is 500.0 m away in a direct line of sight. The moose stands 40.0 m below the horizontal in a depression with a bog at the bottom. The muzzle velocity is 2500.0 feet per second and the sight on the rifle is...
6. ### How would i find the velocity of the ship relative to earth?

Homework Statement A ship sets sail from Rotterdam, The Netherlands, heading due north at 7.00 m/s relative to the water. The local ocean current is 1.50 m/s in a direction 40.0º north of east. What is the velocity of the ship relative to the Earth? Homework Equations Vr=Vs-Vc r=relative...
7. ### Find distance from ramp at which skier lands

Homework Statement A skier leaves the ramp of a ski jump with V=10.0 m/s at 15° above the horizontal. Slope of mountain below ramp is 50°. Assuming air resistance is negligible, find distance from end of ramp at which skier lands. Homework Equations 1. sf = si + vist + ½ast2 2. tanΘ =...
8. ### Angular momentum in a two dimensional world

If we were living in a two dimensional world. would we know about angular momentum of an object?
9. ### Instantaneous acceleration from coordinates?

Homework Statement The coordinate of an automobile in meters is x(t) = 5 + 3t + 2t2 and y(t) = 7 + 2t + t3, where t is in seconds. What is the instant acceleration of the car at time t = 2 s? ANSWERS: A. 10.2 m/s2 B. 9.5 m/s2 C. 7.9 m/s2 D. 15.0 m/s2 E. 12.6 m/s2 Homework Equations ains =...
10. ### Finding the distance between two points in terms of variables

1. A spring of spring constant k is attached to a support at the bottom of a ramp that makes an angle θ with the horizontal. A block of inertia m is pressed against the free end of the spring until the spring is compressed a distance d from its relaxed length. Call this position A. The block is...
11. ### Calculating Impact Speed of a Ball Thrown Toward a Cliff

Homework Statement A ball is thrown toward a cliff of height h with a speed of 28.0 m/s and an angle of 60.0° above horizontal. What is the ball's impact speed Homework Equations Vf=Vi-at Sf=Si+Vit-1/2gt^2 Vy=sintheta Vx=costheta The Attempt at a Solution first find the vertical velocity =...
12. ### Two dimension motion problem

I was given this question as a study question but no solution provided. I am unsure how to solve the question. Homework Statement A man is swimming 3m/s down a river. The man is 50m from the edge and 1000m from the top of the river. If I am in a boat at the top corner of the river...
13. ### Two Dimension Motion Vectors

Homework Statement Suppose the positon vector for a particle is given as a function of time by vector r(t) =x(t)i + y(t)j with x(t) =at + b and y(t) = ct2 + d, where a=1.00 m/s, b=1.00m, c=.125 m/s2, and d=1.00m. (a) Calculate the average velocity from t=2.00s to t=4.00s. (b) Determine...