Trajectory Definition and 467 Threads

A trajectory or flight path is the path that an object with mass in motion follows through space as a function of time. In classical mechanics, a trajectory is defined by Hamiltonian mechanics via canonical coordinates; hence, a complete trajectory is defined by position and momentum, simultaneously.
The mass might be a projectile or a satellite. For example, it can be an orbit — the path of a planet, asteroid, or comet as it travels around a central mass.
In control theory, a trajectory is a time-ordered set of states of a dynamical system (see e.g. Poincaré map). In discrete mathematics, a trajectory is a sequence



(

f

k


(
x
)

)

k


N





{\displaystyle (f^{k}(x))_{k\in \mathbb {N} }}
of values calculated by the iterated application of a mapping



f


{\displaystyle f}
to an element



x


{\displaystyle x}
of its source.

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  1. P

    Teddy Bear Falls: Solving a Trajectory Problem

    At a county fair, a boy takes his teddy bear on the giant Ferris wheel. Unfortunately, at the top of the ride, he accidentally drops his stuffed buddy. The wheel has a diameter of 14.6 m, the bottom of the wheel is 1.1 m above the ground and its rim is moving at a speed of 1.0 m/s. How far from...
  2. A

    An electron in a trajectory motion between the center of two plates

    Homework Statement An electron with an initial velocity of 5.6x107 m/s in the x-direction moves along a trajectory that takes it directly between the center of two 20 cm x 20 cm plates separated by 1 cm. The plates are connected to a high voltage power supply so that the potential difference...
  3. B

    Does recoil affect speed of trajectory?

    Does the mass of a cannon affect the speed at which the ball will leave the barrel? If you produce two equal explosions -- one in which the cannon sits on a frictionless surface, and one in which it is bolted to the ground -- will the cannonball fly further when it is bolted? How would you...
  4. J

    Calculating the trajectory of a projectile

    Homework Statement So, we have a physics project, in which we must build a water balloon launcher and launch the balloon at a stationary target about 50 yds away (normally we use meter, however we are firing on a football field). I have created my launcher (it is basically a slingshot), but...
  5. Telemachus

    Trajectory as a sufrace intersection

    Homework Statement Well, I must express this trajectory: \vec{r}=(t^2,2t,t^2) as an intersection of two surfaces. I really don't know how to work this. It seems to be some kind of parabola, but I'd really like to see some step by step for solving this. Bye, and thanks off course.
  6. M

    Understanding Trajectory Graphs

    Trajectory Graphs?? Homework Statement The trouble I'm having is with determining what information I can get from a trajectory graph and how that information differs from what I can find on a position vs. time graph. Is the acceleration I find just the rate of change in the direction of...
  7. M

    Trajectory Graphs: Direction of Velocity & Acceleration

    So it is my understanding from my book that the information that we can get from a trajectory graph is the direction of velocity, but not the magnitude of velocity. If the tangent line to a point on a trajectory graph just gives the direction of velocity, why can the trajectory graph still be...
  8. X

    Calculating Trajectory & Time of Flight

    Homework Statement See picture Homework Equations Trajectory equation and total time of flight The Attempt at a Solution Okay what would be the best way to approach this? should i find out the distance the ball goes? then subtract 35m to to get my length of hill and use that for...
  9. R

    Trajectory Problem using Newton's Formulas

    Hey. I was not sure if I could post this somewhere else, since this has nothing to do with homework or anything like that. Homework Statement In a Newtonian world: Determine the position of object two, being x, z spatial coordinates and y a time one relative to object 1. Object 1 is (0; y; 0)...
  10. V

    Trajectory question(find spped of impact)

    A golfer drives a ball with initial angle θ = 45 from a tee at the origin. The ball hits a window at height h = 10m a distance D = 80m away. a. Find the initial launch speed v0 of the ball. b. Suppose a second golfer tees off from the same spot at an unknown angle and speed, and...
  11. A

    Is the trajectory of a ball with friction calculable?

    I have written a simulation for school that simulates balls being thrown under the influence of friction. To check if my results are correct, do you know if it is possible to calculate the trajectory? I can use the friction formulas of either stokes or Newton. Is it possible to calculate...
  12. S

    Calculating the highest point of a trajectory

    1. A soccer ball is kicked with an initial actual velocity of 20 ms at an angle of 20 degrees with the horizontal. Find the vertical distance from ground to highest point.
  13. S

    Solving Trajectory Problem with 2 Variables (V,A)

    Homework Statement I was attempting to finish a group project when I noticed certain elements lacking in it. I am attempting to graph the below equation but I can't get it to work. It has two variables, V(Velocity) and A(time in this case). So I am trying to figure out how I can graph this...
  14. M

    Inverse kinematics for object trajectory in 2D (control theory?)

    Drone - grey, Asteroid - brown. The goal is to steer the drone into the asteroid. The force acting upon the drone ("thrust") for movement can be in any direction, varies in magnitude, and can be applied at any discrete point in time. The drone's future location is deterministic. I'm confused...
  15. A

    Finding the Optimal Flight Path to the Origin: A Vector Addition Problem

    Homework Statement A pilot attempts to y with constant speed v from the point P = (D; 0) on the x-axis to the origin O = (0; 0). A wind blows with speed w in the positive y direction. The pilot is not familiar with vector addition and thinks the shortest path to O is achieved by ying his...
  16. T

    Bullet trajectory; solving for required angle of elevation

    Homework Statement Bob is trying to hit a stationary target 146.00m downrange, his eyes are 1.8m above the ground, firing from a standing position. The muzzle velocity of the projectile is 382.524m/sec (1255 ft/sec), wind is negligible; at what firing angle must he fire to successfully hit the...
  17. S

    Calculating Projectile Trajectory Without Air Resistance

    Greetings, Before I begin my problem, I would like to confess that I understand almost nothing about physics. My math is limited to what I am doing in class right now as a ninth grader ( I understand quadratics...). I am doing a research project, and I need some help. Homework Statement...
  18. R

    Plot 2D Trajectory: Solve Initial Velocity & Coordinates

    I'm trying to plot out the trajectory of an object in a program that is looping through the function and spitting out the x and y coordinates, but I'm having trouble. I want to see a parabola starting at 0,0 going up and ending again at x,0. Basic question: (units aren't critical here f/s m/s...
  19. M

    Understanding Hyperbolic & Parabolic Trajectories

    Hi, I'm trying to wrap my head around the different kinds of trajectories. Firstly, what kind of objects have hyperbolic trajectories? And how do we differentiate between a parabolic trajectory and a hyperbolic one? Thank you for any help. Maria
  20. D

    Angle of a trajectory required to make it go a specified distance?

    Here is the problem at hand: A gun has a muzzle speed of 100 meters per second. What angle of elevation should be used to hit an object 180 meters away? Neglect air resistance and use g = 9.8 m / sec^2 as the acceleration of gravity. I attempted to solve this by calculating the time...
  21. A

    Which Coordinate-Based Model Best Suits Trajectory Simulations?

    Homework Statement I have an assignment in which i need to employ the practice of 'Crowd Sourcing' to get the answers to problem statements. I can have my own answer but i also need the answers collected from various sources. *Kindly help ur answers* The problem statement is ...
  22. K

    Trajectory of a particle in a field (special relativity)

    Hi, I'm new on this forum and I would like to say hello to everybody! I have a problem with homework from my "Basics of theoretical phisics" class. Homework Statement I have to find a trajectory of a particle in field of force: F = - \frac{\alpha}{x^2} Homework Equations I was...
  23. S

    Computing Meteor Trajectory from Data for Two Stations?

    I'd like to compute a meteor trajectory from data gathered by two video camera. One method I've recently considered but do not know much about it is to treat the meteor as an Earth satellite in a circular orbit. Once a great circle plane is found, then one could produce a ground track by...
  24. B

    Trajectory of charged particle moving in a magnetic field

    In this video here are those pink green the magnetic field lines? If so where does the proton come from? If I'm not mistaken a charged particle in motion will only be influenced by the magnetic field if its not moving parallel to the magnetic field lines but in this video the proton appears to...
  25. I

    Mastering 3D Trajectory for FPS Game Designers

    Hello, I am designing a FPS in which I am planning for the trajectory of a bullet to follow this formula here: http://en.wikipedia.org/wiki/Trajectory#Derivation_of_the_equation_of_motion" I am not adding any drag or resistance a the moment, but the problem is, that all these trajectory...
  26. I

    Calculating Position on a Trajectory - Derivation of Equation of Motion

    I have never taken any physics course before, but I am designing a game in which the projectile(bullet) is going to drop over time. I want to know which equation do I use to calculate the position on a trajectory. Given that I have the angle, and initial velocity...
  27. A

    Spinning ball bounces off ground, following curved trajectory

    Homework Statement You have a solid, homogenous ball with radius R. Before falling to the floor, its center of mass is at rest, but it is spinning with angular velocity \omega_0 about a horizontal axis through its center. The lowest point of the ball is at a height h above the floor. When...
  28. B

    Projectile Trajectory (I'm confused about the lab report)

    The experiment was to measure muzzle velocity of a ball fired by a 'spring gun'. Then to use the equations of projectile motion in order to determine the projectile trajectory. During the experiment we used a variable-height platform to stop the ball mid-air (at y = 0.4 m & y = 0.1 m). Now we're...
  29. J

    What are the equations for trajectory in an E-field?

    Homework Statement Hello, I have a physics exam on friday. My teacher said one of the questions would be on the TRAJECTORY (of an electron) IN AN E-FIELD. he told us to remember than tanß = sinß / cosß we haven't used tan, sin or cos during class work. I was hoping someone could give me a...
  30. R

    Parabolic Projectile Trajectory

    Hi, Im currently working on a video game, and have come to an aspect that I'm very unsure about (I'm self taught in most of my game physics knowledge, so there are quite a few gaps). Let's say there is an environment with no features that act on objects except for gravity (or simply no wind...
  31. X

    Calculating angle for trajectory with exit position not at 0,0

    I'd like to calculate the angle to shoot a projectile from a cannon in order to hit a target. However, the position that the projectile will be exiting from will not be at 0, 0 -- it will vary according to the angle of the cannon itself. The projectile will be exiting from the tip of the cannon...
  32. R

    Definitoon of trajectory in quantum physics, especially in path integrals

    What is the correct way to use the term trajectory in physics when discussin path integral forumaltion calculations. Here is the sentence i am trying to complete and am unsure if i may use the term trajectory: So the wavefunction offers a much more simplistic and perhaps more beautiful way to...
  33. E

    Finding Constants in Relativistic Trajectory Problem

    Homework Statement Given that the trajectory in frame S is: x=\frac{c^2}{a}(\sqrt{1+\frac{a^2t^2}{c^2}}-1) Show that in S' that is moving in the +x direction at speed u: x'=\frac{c^2}{a}\sqrt{1+\frac{a^2(t'-A)^2}{c^2}}-B Find the constants A and B. Homework Equations Lorentz...
  34. I

    One question about Parabolic and Hyperbolic trajectory.

    In the Parabolic and Hyperbolic trajectory.Is the sun in the focus point of parabola and hyperbola?
  35. I

    Orbital energy of ellipse and hyperbolic trajectory

    Please tell me how to find the orbital energy of ellipse and hyperbolic trajectory. Thank you.
  36. S

    Particles trajectory in a bound orbit.

    Homework Statement I am to find the particles trajectory to the first order of r/a knowing it to have the Yukawa potential v(r)=V_{\circ}r_{\circ}/r * e^{-r/r_{\circ}} = -k/r * e^{-r/a} Homework Equations \theta(r)= \int (1/r^{2})/\sqrt{2\mu (E-U-l^{2}/2\mu r^{2}}) dr...
  37. P

    Parametrize trajectory of a hocjey puck

    Homework Statement A hockey puck of radius 1 slides along the ice at a speed 10 in the direction of the vector (1,1). As it slides, it spins in a counterclockwise direction at 2 revolutions per unit time. At time t = 0, the puck’s center is at the origin (0,0). Find the parametric equations...
  38. P

    Parametric equations for trajectory

    Homework Statement A jet takes off from (1, 1, 0) at time t = 0 and moves with constant speed v = (−5, 0, 1). In a flight simulator, the trajectory of the jet is displayed in the yz-plane as it would appear to an observer at the point (1, 0, 0). Find the formula (in the form y = y(t), z =...
  39. F

    Highest point on trajectory of tennis ball

    Homework Statement A tennis ball is thrown toward a vertical wall with a speed of 21.0 m/s at an angle of 40.0 degrees above the horizontal. The horizontal distance between the wall and the point where the tennis ball is released is 23.0 m. a. At what height above the point of release does...
  40. R

    What Is the Launch Angle of a Ball Thrown Against a Wall?

    Homework Statement A ball is thrown with initial velocity 20m/sec against a wall 50 meters away. It is released from a height of 1.8 meters, and hits the wall at 1.2 meters. Find the angle of the throw. Homework Equations 50=20t*cos(theta) -.6=20t*sin(theta)-.5(9.8)(t^2) The...
  41. L

    What is the path of a particle on an inclined plane with a string attached?

    Respected experts, I am in need of your help. Here goes the question: "A particle is placed on a rough plane inclined at an angle theta, where tan θ = μ = coefficient of friction(both static an dynamic). A string attached to the particle passes through a small hole in the plane. The string is...
  42. K

    Argument with professor: how can you describe the trajectory of a particle?

    I had a physics test last week. When I got the results, there were some correction mistakes in my opinion, so now it's being revised. I had a small disagreement with my professor over one of the theoric exercises, and tomorrow i'll probably be having the same argument again, so I thought of...
  43. G

    Trajectory and Force Problem: shot putter launch

    Homework Statement A shot putter launches a 7.22 kg shot by pushing it along a straight line of length 1.84 m and at an angle of 33.0° from the horizontal, accelerating the shot to the launch speed from its initial speed of 2.3 m/s (which is due to the athlete's preliminary motion). The shot...
  44. M

    Lunar Crash Trajectory Problem

    Homework Statement As a command module, orbiting the moon passed through a point A (120km altitude), it released a lunar excursion module, which crashed into the moons surface at point B. Knowing the angle AOB was 50 deg (where O is the centre of the moon), determine the velocity of the lunar...
  45. CFDFEAGURU

    New Calculated Trajectory for the Apophis asteroid

    Hello all, This NASA press release indicated that there is less likely hood of an encounter with the Apophis asteroid in 2036. http://www.nasa.gov/home/hqnews/2009/oct/HQ_09-232_Apophis_Update.html Thanks Matt
  46. P

    Solving Trajectory Problem: Initial Speed, Time, & Height

    Homework Statement A college regulation goal post has a horizontal ball at a height of 3.048 m from the ground. A kicker attempts a field goal at a distance of 30 m from the goal posts. The initial speed of the ball is 19 m/s making an angle of 40 degrees above the horizontal. The plane of...
  47. R

    Trajectory of a squirt of water to hit a fly

    Paradoxical Algebra: Trajectory of a squirt of water to hit a fly Can ANYONE explain to me why 3 perfectly algebraically sound procedures all give me a different answer, where only one gives me the correct answer? Also, can you disprove the 2 wrong procedures (IE: As I said before, tell me why...
  48. R

    Trajectory of a Baseball: Will it Clear the Fence?

    Now I'm seriously just tired and can't get these, but I don't know why this is wrong at all. This would help if I had a study partner in my physics class (to bounce ideas off of), but no one else in my class is overly strong in the subject. Homework Statement A batter hits a pitched ball...
  49. D

    Finding Speed and Angle of Projectile Trajectory

    Homework Statement A diver leaves a 3m board on a trajectory that takes her 3.0m above the board, and then into the water a horizontal distance of 3.0m from the end of the board. At what speed and angle did she leave the board? Homework Equations Vf^2=Vi^2 + 2ad Y=Y0 +VyT - 0.5gt^2...
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