Trajectory Definition and 467 Threads

Hi, Just starting to learn kinematics and the book says that from the kinematic equations of motion: x=ƒ1(t) ; y=ƒ2(t) ; z=ƒ3(t) we can "eliminate de time" from the above and get: F1(x,y,z)=0 ; F2(x,y,z)=0 -> aka. trajectory eq. their "ensemble" being 2 surfaces giving the trajectory...

I have a physics degree, I'm now retired and have taken up long range shooting as a hobby. When shooting at 600 yards, my spotters have noticed the contrail of my bullet follows a helical trajectory near the target. I shoot a 243 (6mm), 105 grain target bullet made by Berger at a muzzle...

Homework Statement I am given that an object of mass m has an attractive force F=-A/x^2 acting on it, where A is a constant and x>0. I need to find the potential energy. After i need to suppose initial conditions (x0, v0) such that total energy=0. I need to find the trajectory x(t) with v>0...

Homework Statement ball is thrown at slighta angle upwards and to the right. Angle between horizontal and the launch velocity vector is 35deg upwards. Launch velocity vector (v_0) has magnitude of 12m/s Only gravity affects the ball as a force. (no air resistance) t_0 = 0 secs t_1 = 0.2 secs...

Hi all, I need to trace the trajectory of a moving object. The object are yellow and opaque while the background is grey. Since I'm interested in the shape rather than the exact coordinate, I'm wondering if I could use the light painting principle to impress on a photo the trajectory. How could...

Hi! I hope I'm posting in the correct section. I found this very similar topic in this forum: https://www.physicsforums.com/threads/orbital-ellipse.482713/ Aside from very helpful formula for calculating semi-major axis, the question was left unanswered. I have a working simulation of...

Homework Statement Consider the pendulum depicted in the adjacent figure: a mass m is attached to non stretching chord of length `. Directly below the pendulum is a circular disc rotating with constant angular velocity w. We attach to the disk a frame whose x-axis is in the plane of the...

This is a famous experiment conducted by Rutherford, in this exprement, the alpha particle(+2e charge) repulsed from necleus by coulomb force, and eventually divert its trajectory by theta. I want to show the trajectory of alpha particle has asympotes which means it go out along that asympote...

Homework Statement A ball is shot from ground into the air. at height 8.3m, its velocity is 7.8i + 6.5j. Find Maximum height rise, horizontal distance traveled and magnitude of velocity just before the ball hits the ground. Homework EquationsThe Attempt at a Solution So i got the total...

Hello. It is said that if we exchange two electrons, we can't tell which is which. Identical mass, charge, etc. So if I hold two electrons, one in each hand, and someone switched them, I wouldn't be able to know. But one way to distinguish particles is their trajectory. If I have a very long 1D...

I have a basic question about the trajectory of a photon. As can be seen in the figure above, let's suppose there is a stationary frame F and a cylinder sealed with two sided mirror is located at the origin of F. Then let's consider two cases; First is the velocity of cylinder is 0 with...

MX''=Fn(cosΦ−usinΦ) MZ''=Fn(sinΦ+ucosΦ)−Mg MΦ''=Fn(Bxx+uBz) I tried using Runge-Kutta methods to approximate motion equations in MATLAB but it turn out wrong. I also tired finding and researching forums and web for solution but to no avail. Fn,M,θ,u is constant fn/M = 0.866 it seems that i...

Homework Statement "Upon spotting an insect on a twig overhanging water, an archer fish squirts water drops at the insect to knock it into the water (Fig. 4-38). Although the fish sees the insect along a straight-line path at angle Φ and distance d, a drop must be launched at a different angle...

A stream of water from a water hose can be modeled by the graph of y= -0.003x^{2}+0.58x+3 where x and y are measured in feet. a firefighter is holding the hose 3 feet above the ground, 137 feet from a building. will the stream of water pass through a window if the top of the window is 26 feet...

Homework Statement Two towns A and B, are situated directly opposite to each other on the banks of a river whose width is 8 miles and which flows at speed of 4 mi/hr. A man located at A wishes to reach town C which is 6 miles upstream from and on the same side of the river as town B. If his...

Hi all! I'm super lost on this homework question. I tried asking the professor but was kind of brushed to the side. My vector calculus knowledge is pretty limited (I had an unfortunately experience in that class). Anybody have any ideas on how to go about solving for this? It's a problem out of...

What would be the propable trajectory and position of the ninth planet that has been suggested few days ago (20.1.2016 by Konstantin Batygin and Michael E. Brown) ? if i understood correctly, the exact position of the planet is unknown and has not been evaluated. But by looking this article...

Hi everyone, Firstly, sorry if this seems a bit rushed, I don’t have much time in between shifts at work. You may have to refer to my links. But if needed, I will add more information later on. I've been racking my head over this for the last month or so. I’m kinda doing a private personal...

Homework Statement http://imgur.com/RDMG4Pj Link to drawn out problem^ The ball goes through the hoop NOT at the peak, but rather on it's downward path. It's asking for the total x-displacement, launch angle (theta), and the total flight time. It must me solved WITHOUT using the range...

Homework Statement Given the force ## \vec{ F }(x) = (-12x + 6) \vec{i} ## ; find kinetic energy ## T## at the point ##x=2## and trajectory of a particle ## \vec{r}(t) ##, given that ## \vec{r}(t=0)=\vec{0}## and ##\dot{\vec{r}}(t=0)=\vec{0}## . 3. The Attempt at a Solution Since...

Homework Statement Carbon scatters on a proton. What is the limit of the angle of scattering? I'm not really sure where to start this question. I know it has something to do with Rutherford Scattering and impact parameter. Homework EquationsThe Attempt at a Solution

Hello PFers, I'm trying to make a program in java which process user's position, initial velocity of the projectile and the elevation of the projectile and show the trajectory in GUI. The language is in java. The problem is, the trajectory won't show. It is supposed to show the player's...

How can I find an equation to calculate the lift coefficient on a basketball at different launch velocities? I looked at different papers explaining the physics of basketball throws but all i could find was an equation for the drag coefficient: -mv +1/2 ρ A Cd v^2 = mv

Homework Statement A particle moves along a closed trajectory in a central field of force where the particle's potential energy is U=kr2 (k is a positive constant, r is the distance of the particle from the center O of the field). Find the mass of the particle if it's minimum distance from O...

Hey I am trying to tweak a Fighter jet game to make it more realistic. I am trying to the US Air Force AIM-120D AMRAAM missile like what it can do in real life. The question is what is the effective range of the missile against a maneuvering target or evading target, for a fighter let say 6Gs...

Homework Statement A projectile is fired from a cannon at X-distance of 25m (X=25), height 10m (y=10), and fixed angle (53-degrees). After 3 seconds, the projectile hits its mark at different height 50m (y=50), and at a range of 175m (X=200). Gravity is normal and there is no wind resistance...

Homework Statement I am trying to find the force needed from a spring to launch a mass of 800g to a length of 0.875m. This launch would be at the optimum angle of 45º. I am aware of all projectile motion equations but am having difficulty linking them to force and thus solving the problem...

My textbook said that field lines do not always represent the trajectory of a charged particle in a field. How would you find the trajectory then?

Hello folks, I need some physics help. Some background to get us on the same rails :) I am developing a 2D game in my spare time. Player controls an object (aka spaceship) in open space (no gravitation influence) by selecting a point in space. A constant force which is always pointed at the...

Homework Statement Upon spotting an insect on a twig overhanging water, an archer fish squirts water drops at the insect to knock it into the water (Fig. 4 -38). Although the fish sees the insect along a straight-line path at angle f and distance d, a drop must be launched at a different angle...

Homework Statement A boy kicks a ball with an initial velocity v0 that forms an angle of 30° with the x. The ball, at the culmination of the trajectory, enters a window at a height of 9.8 m. Find the module of the initial velocity and the time used by the ball to reach the window. Also find the...

why does light travels in a straight line?

Homework Statement A football player releases a ball at 35° with initial velocity of 80 ft/sec. Determine the radius of curvature of the trajectory at times t = 1 sec and t = 2 sec, where t = 0 is the time of release from the quarterback's hand. For each case, compute the time rate of change...

Homework Statement Determine the time it takes for the ball tor each the plane of the fence. Answer in units of s. (VIEW IMAGE ATTACHED) Homework Equations Vf+vi+at d=vit+.5at^2 vf^2=vi^2+2ad The Attempt at a Solution [/B] I found Vix to be 11.59 using trig. I then used the second equation...

Homework Statement A particle travels between two parallel ver- tical walls separated by 25 m. It moves to- ward the opposing wall at a constant rate of 9.2 m/s. It hits the opposite wall at the same height. The acceleration of gravity is 9.8 m/s2 . (IMAGE FOR CLARIFICATION ATTACHED) a)...

Homework Statement An artillery shell is fired at an angle of 23.9◦ above the horizontal ground with an initial speed of 1530 m/s. The acceleration of gravity is 9.8 m/s2 . Find the total time of flight of the shell, neglecting air resistance. Answer in units of min. Homework Equations...

Homework Statement Sketch the trajectory over the time interval 0 ≤ t ≤ 10 of the particle whose parametric equations of motion are given by X= t−3sint . And y = 4 − 3cost find the value of x,y,t Remember that you should be in Radian mode! Answer Do you isolate the t first and plug it in...

So, I've been reading through "Exploring Black Holes: Introduction to General Relativity" by Wheeler and Taylor, and I've had some ideas I wanted to pursue and do some research in regarding trajectories within the event horizon. In this, I'd like to have the mathematical tools to investigate...

Hi all, This question just occurred to me: Whether a falling raindrop in presence of a uniform horizontal wind (ideally speaking) has a curve trajectory or a straight line? Assuming the wind force is constant, the velocity of the raindrop in horizontal direction will keep on changing since there...

Homework Statement : The trajectort of two projectiles are shown in the figure. Let T1 & T2 be the rime periods and U1 and U2 be their speeds of projection. Then(state the answer with REASON): A) T2 > T1 B) T1 = T2 C) U1 > U2 D) U1 < U2 [/B] (MAYBE, MORE THAN ONE CORRECT) Homework Equations...

Homework Statement I have 2 perpendicular oscilations and I have to find the trajectory equation. $$x=A\cos\omega t\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, (1)$$ $$y=B\cos(\omega t+\Delta\phi)$$Homework Equations $$\cos (x+y) =\cos x\cos y -\sin x\sin y$$ $$\cos^{2} x+\sin^{2} x =1$$...

Hello everyone, I have been interested in trajectory optimization for a while now and I have read a few papers on that topic and bought the book "Spacecraft trajectory optimization" from Cambridge University Press and want to start programming with the goal to optimize a trajectory in a...

Homework Statement I am asked to find r(t) for a charged q particle in an magnetic undulator. Wrote down these equations: x'' = w* y' *cos(a*x) (1) y'' = -w* x' *cos(a*x) (2) z'' = 0 (3) r(0) = (x0, y0, z0); r(0)' = (x0', y0', z0'). Homework Equations Not sure how to go on solving these...

How an electron moves when it is released from rest to a positively charged hollow cylinder? The hollow cylinder is finite and insulating. The electron is constrained to move only in z direction (into the center of the hollow cylinder). My thinking is that there is no electric field inside the...

Greetings PF, I'm a computer science student who is tasked with a robotics project. I've got a 2-wheeled robot (there's a 3rd dummy wheel on the back to prevent it from falling over) that turns like a tank, by means of turning one wheel faster than the other. If both wheels are the same speed...

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown > Hello, I'v been trying to find an answer for this question for quite some time, I always hit a complex trigonometric equation or a 4th degree polynomial equation. any help would be very much...

So I wanted to get some second opinions on this situation I have thinking about.Lets say an electron enters, normally, a section of bfield that is perpendicular to its motion such that the electron will undergo circular motion. This is the simple part and is labeled as "E0" in the picture...

Hi all. I am not quite sure if this is the right forum to place this question but for me there are several forums that would fit with my situation :D I am making a game where I have to throw/shoot a projectile through a 3 dimensional space which has to land on a specific object. There are...

In this problem, I need to find the trajectory of a particle (as a function of time) which moves at a speed 's' but also turns at an increasing rate; angular acceleration α. The trajectory looks like a spiral which converges to a point. The particle has an initial position vector p and a...

Homework Statement Lower surface of a plank is rough and is initially at rest on a horizontal floor. It's upper surface is smooth and has a smooth hemisphere place over it through a light string as shown. Find the trajectory of centre of mass of the sphere after the string is burnt. Homework...