Trajectory Definition and 446 Threads

Okay, so I am a team member of a college robotics team, and this year we have quite challenging theme of playing badminton with robots, so for this reason we decided to track the position of shuttlecock in air. Now our approach was to predict the final position where it will land on ground from...

Here is the picture for you to understand it better. Please help me calculate the velocity required for the ball. I have already tried it with the formula: displacement = initial velocity(time) + (acceleration)(time2)/2 but cannot since I do not know the initial velocity and the time Please...

Can anyone point me in the direction of any published scientific work involving the study of Earth to Mars flight trajectories? I am thinking of researching this topic for a project and I would like to know about the work that has already been done.

< Mentor Note -- thread moved to HH from the technical physics forums, so no HH Template is shown >[/color] So the problem that I have been assigned has formulas of rotational energy, momentum, trajectories, inertia, and inclined planes. A solid sphere is rolling down an inclined plane (that is...

Homework Statement The problem and my attempt are attached Homework Equations Chain rule for partial differentiation perhaps And basic algebra The Attempt at a Solution I'm unsure of how to approach this but I differentiated all the expression at the top.

Consider the release of a single photon or electron into a vacuum. The particle will have an initial trajectory. How is it possible for this event to give rise to a wave that has a continuously changing trajectory?

If you throw a ball obscenely high (ignoring air resistance, etc), and the Earth is rotating, the ball will land in a different spot. Relative to an observer on the Earth, the ball has a sub-orbital trajectory across the surface. If we attach thrusters onto that ball, and have it burn at its...

Hello, and +1 for this great forum! I have encountered a small problem in my way of creating a small game. I have a snowball that is being thrown by the player. The dynamic variables from the input of the player are: Force and angle (between 90 : -90 degrees). At the moment I apply the force...

Homework Statement Euler method : Plot the trajectory of a body moving under the influence of the suns gravity from initial conditions x=1, y=0, vx=0, vy=1. My trouble is figuring out my function. Homework Equations d2r / dt2 = -r/r3 The Attempt at a Solution What I have been doing...

Homework Statement [/B] You are given a particle, with the trajectory of a circle, with radius of 3 meters. The particle moves clock-wise, and when t=0, the x, y coordinates are (0, -3). Find parametric equations for the coordinates (x, y) in terms of the parametric t (time). Homework...

Homework Statement This is just a project for fun, not homework. I'm writing something in python that takes in an apple's initial position vector and initial velocity vector, and for a given gravitational field due to a planet, returns the next position vector after a small time increment...

Hi all. This may be a stupid question to some.. But please do answer it. Why do planets move in an elliptical path? Why only ellipse? Or even a circular path for approximation? Why not a path which has corners? Like an octagon or a square?

http://puu.sh/dc1YU/fa1e0f3a6e.png Hey so if we have a trajectory like this, where would it be maximum speed? From what I understand, at the midpoint, v = 0 right? So would the maximum speed be in between the bottom (initial) and the centre of the trajectory (peak), represented by B in this...

Homework Statement I want to derive an equation for the place where airdropped bomb is going to hit the ground. Known data at the moment of drop: 1) position [x,y,z] also and the pitch angle (between the airplane's axis and the ground - we assume that Earth is flat) 2) linear and angular...

I am curios about trajectory programs (but not weather) the real particle movements.If you know How can I get it (but free) I will be happy Thanks

Homework Statement A bullet (3.40g) has a velocity of 160m/s perpendicular to Earth's magnetic field 5x10^-5 T . The bullet has a charge of 13.5 x 10^-9 C.With what distance will it be deviated from its trajectory after it has traveled 1.00km? Homework Equations...

Hello. I was told that "in QM the information doesn't disappear". Does it mean that, in QM, the trajectory in the phase-space can't split? [The typical example is a vertical simple pendulum, with the mass above the spin-point; in classical mechanics you can't know if the pendulum will fall one...

Homework Statement Homework Equations 1/2mv^2, mgh, and basic kinematics equations The Attempt at a Solution I set the height = 0 at moment before the launch. To get the velocity, I used: energy before the ball starts accelerating (PE) = energy right before the ball leaves the ark (KE)...

Homework Statement A body is moving, with the following data (these are all dependencies of the radius vector components respective to time): x(t)=At2, A>0; y(t)=Bt, B>0, z(t)=0. How does the trajectory of this movement look? Homework Equations r=x(t)i+y(t)j+z(t)k Velocity=dr/dt The Attempt at...

so suppose i have a wire given parametrically by C(t)=x(t),y(t),z(t), and i run a current of I amps through it. to find the total B field i would sum up the contributions over the length of the wire, and (please tell me if I am wrong) the total B field due to the wire at point p=xp,yp,zp would...

Homework Statement Find the optimal trajectory x*(t) that minimizes: J = \int_{0}^{1} \left( \frac{\dot{x}(t)^2}{2} + 3x(t) \dot{x}(t) + 2x^2(t) + 4x(t) \right) dt with x(0) = 1 and x(1) = 4 Homework Equations Euler's equation: \frac{\partial g}{\partial x} -...

So, I'm attempting to programm orbit in Unity game engine. So I need equation that shows r and phi depending on time. Equation for gravitational potential is U(r)=-k/r+M^2/(2*μ*r^2). Force is -1*derivation of U(r) by r. So I get lots of stupid stuff. If anybody could help me to...

Facing some horrible mathematical situation while solving to find equation of trajectory of projectile when drag is proportional to v^2. my equations where i end up with are as follow: equation 1: mdv/dt=(-kv^2)+(-mgsinγ); equation 2: (-mv)dγ/dt=mgcosγ; equation 3: dx/dt=vcosγ; equation...

Homework Statement The uniform 45.6 mT magnetic field in the picture below points in the positive z-direction. An electron enters the region of magnetic field with a speed of 5.29E+6 m/s and at an angle of θ = 30.1° above the xy-plane. Find the radius r and the pitch p of the electron's spiral...

I am trying to find the formula for the so called "ballistic loophole" which is a technique where one will cut a small hole in a wall or structure (no bigger than 3 inches wide or tall) and shoot through it at a target without placing himself to close to the wall. I know I need the height...

Homework Statement A baseball with a mass of 0.125 kg is moving horizontally at 32.0 m/s [E], when it is stuck by a bat for 0.00200 seconds. The velocity of the ball just after the collision is 52.0 m/s [W 20 N]. Homework Equations p = m Δv Fnet = ∆p/∆t there are also these...

On page 122 of Born and Wolf's "Principles of Optics" the following equation for the trajectory of a ray of light is glibly derived in association with the eikonal equation. \frac{d}{d \bf s} (n \frac{d \bf r}{d \bf s}) = \nabla n where n is the index of refraction and r is the displacement...

Hi there guys. As the title implies I'm trying to draw a trajectory on the screen (yes, this is indeed about programing :P) involving multiple sources of gravity. Here is my dilemma: Since I'm working with an update loop there would be no problem to just simulate an object and having it...

Hello Forum, Let's consider a particle that is giving an initial speed in a certain direction. The particle is now moving in that initial direction at a constant speed. If a later moment a force starts acting on the particle and the force direction is not along the original particle...

Homework Statement mass = 100 Kg Cross Area = 4 Drag = .4 Initial velocity = 17.59 m/s Gravity = 9.81 Angle Changes according to the position of the mouse Terminal velocity = 31.649 ; Don't know if its relevant but I calculated this Homework Equations Y1 :=...

Homework Statement A boat part from the point P of the bank of a river, with width D, and that flows with a constant velocity VR, and moves with a constant velocity VB, directed towars a point Q, located on the other side of the river directly in front of P. If r is the instantaneous distance...

Can someone please explain to me what a "dynamical trajectory" means? I am reviewing the first chapter of my classical mechanics book (Fetter & Walecka), and in the very first section he uses the term "dynamical trajectory". I have seen this derivation many times, but I just don't understand...

Ok, I am a bit stuck on a homework problem. I know the following: Initial speed: 25 m/s Distance: 49.85 m Initial height: 30 m And that is it. I know that one possible initial trajectory is 70 degrees, but I need to find the other, and that is where I am having a problem. Of the equations that...

Homework Statement Show that for any trajectory r(t) the acceleration can be written as: \mathbf{a}(t)=\frac{dv}{dt}\hat{T}(t)+\frac{v^2}{\rho}\hat{N}(t) where v is the speed, T is a unit vector tangential to r and N is a unit vector perpendicular to T, at time t. rho is the radius of...

I am attempting to create a spreadsheet that models the flight path of a sphere. My model should consider air resistance, but I've opted to ignore magnum. As a resource to help me, I'm using http://www.team2834.com/team_documents/Projectile_motion_with_air_resistance.pdf, but I have ran into...

Can you please explain why the paths of objects are hyperbolic, parabolic and elliptic for energies positive, zero and negative respectively?

Hello Everyone, First time posting on this forum and looking forward to see what you guys can teach me! I am working on a program for a Raspberry Pi as a controller for a mechanical rotary and need some help from you physics enthusiast out there. Looking for some insight on the calculations...

background information is that I have been working on code for a rocket launch to the ISS and I have gotten it close. The problem is when calculating the Force of drag, the problem occurs with it. As entering space, and for this "model" were going to say that temperature is 0 K in space or...

Homework Statement A cannon shoots a ball at an angle \theta above the horizontal ground a) Neglecting air resistence, find the ball's position (x(t) and y(t)) as a function of time. b) Take the above answer and find an equation for the ball's trajectory y(x).Homework Equations...

Homework Statement A projectile is launched from the earth’s surface at initial speed vi at angle θ0 with the horizontal. When the projectile is at its maximum height h, it has half the speed it had when it was at half its maximum height h/2 At what angle was the projectile launched...

1. How to get x,y positions for a tennis ball at each time t given total force exerted?2. We consider Drag force D, Lift Force L and Gravitation force W D=1/2*(0.55+1/((22.5+4.2*(v/(w*R))^2.5)^0.4))*pi*R^2*d*v^2 L=1/2*(1/(2+(v/(w*R))))*pi*R^2*d*v^2 W=m*g as described in...

Homework Statement "In a movie scene involving a car chase, a car goes over the top of ramp A and lands a B below. Determine the speed of the car at A if the car is to cover distance d=180ft for \alpha =15° and \beta = 30°. Neglect aerodynamic effects. Homework Equations Word.doc is the...

Rusty on the math... I am working on a problem and need the derivation of a free fall trajectory for an object at a distance above Earth where the change in acceleration is not negligible. How do I integrate the distance/ acceleration formula taking into account the change in g to get the...

I'm hoping you can help with a debate I'm having with a friend regarding whether throwing a ball in a headwind is the same or different from throwing a ball from a moving platform (lets say an open boat). If you want some numbers, could you please work with these: For the static throw, can...

To what extent do phase space trajectories describe a system? I often see classical systems being identified with (trajectories in) phase space, from which I get the impression these trajectories are supposed to completely specify a system. However, if you take for example the trajectory...

I have been trying to find a hyperbolic trajectory that has hyperbolic excess speed of 3.944 km/s. However, I can only find ones that would start inside the Earth's crust. mue = 398600 energy = mue / (2 * a) ve = 29.78 vinf = 3.944 = \sqrt{mue / a} I have at least 30 more...

Hey ya'll ... I just need clarification on this solution. Is it correct in me saying the vertical component is negative as the ball is falling to the ground? Also, I was unsure whether to use the vertical velocity or release velocity in finding the highest point of trajectory Q: A polo ball is...

I'm working on a project for myself in regards to atmospheric reentry. I've come across some equations that describe the reentry trajectory. I decided to derive the equations using the diagram shown in the attached picture. Are these correct? The reason why I'm asking is that I'm getting small...

A spacecraft is on a hyperbolic orbit relative to the Earth with $a = -35000$ km and an eccentricity of $e = 1.2$. At some initial time $t_0$, the spacecraft is at a true anomaly of $\nu_0 = 20^{\circ}$. At some later time $t$, the true anomaly is $\nu = 103^{\circ}$. What is the elapsed...

Hi! Can someone please explain how does the limit in the attachment equals the curvature of a trajectory? I do not understand it. Why is it defined this way? ζ=dx/dl and it is in the direction of T. Thank you!