Trajectory Definition and 467 Threads

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!

http://i47.tinypic.com/mt55s7.jpg -See for image You drop a ball on this vertical parabola with point A as starting point and point B as ending point. What is the expected natural movement of the ball that is set into motion with no external force assuming no friction? Would it go all the...

Homework Statement A proton moves in a spiral path when enters a magnetic field of 5 T. If the pitch is 5 cm, find the angle between v and B. Homework Equations F = B q v sin θ F = m v2 / r The Attempt at a Solution I am guessing that I need to break down the velocity into two...

Homework Statement A particle of charge −q is moving with a velocity \vec{v}. It then enters midway between two plates where there exists a uniform magnetic field pointing into the page, as shown in attached image. (b) Compute the distance between the left end of the plate and where the...

Okay bear with me here because this might get disgusting. But I was watching Henry's video on how astronauts went to the bathroom in space, and basically they did it in a bag, and shot the bag outside into outerspace. And then he mentioned that the trajectory would change(but extremely small yet...

I am familiar with standard distance-time models for paths of projectiles in perfect conditions, ie, where the curvature doesn't play a role, and where gravity is constant no matter the height. My question is what if you launch a projectile so high that the curvature of Earth plays a role, and...

Need some guidance on how to approach the following scenario Object : 200 grams movement axis : x, y, z distance : 20 meters speed : 70 to 150 kmph adjustable. The plan is to have 3 motors on a jig to control the movement on 3 axis. The issue is to reach 50 m/s speeds and...

Main question in the title. I did a group work in analytic mechanics about pendulum in rotating reference frame and stumbled upon this one: http://peer.ccsd.cnrs.fr/docs/00/50/17/84/PDF/PEER_stage2_10.1016%252Fj.ijnonlinmec.2008.03.009.pdf. Does this always hold? In my solution, there are two...

"After a shell explodes at the top of its trajectory, the center of gravity of the fragments has an acceleration, in the absence of air resistance, equal to g and downward." Why isn't there an x-component? I get why there would be a downward component with a = g, but shouldn't there at...

I've been studying this rather interesting article about projectile motion in special relativity. The thing is, I can't understand how the author found the trajectory function. He says that he did it by solving the following parametric equation: x(t)=\frac{cp_0cos\theta}{F}ln\left \{...

Homework Statement Electrons (mass m, charge –e) are accelerated from rest through a potential difference V and are then deflected by a magnetic field B that is perpendicular to their velocity. Find the radius of the resulting electron trajectory. Homework Equations F=\dfrac{mv^2}{r} F=qvBThe...

Hello, How may I plot the trajectory of a particle whose movement vectors are given as: x(t) = Rwt - Rsin(wt) y(t) = R - Rcos(wt) I have tried squaring both x and y and adding them, to infer some sort of circular trajectory, to no avail. Could someone please assist/make a suggestion?

Feynman_Lectures_on_Physics_Volume_1_Chapter_11 In paragraph 11-6 he says that the tangent acceleration is the change of speed v but if I look at fig. 11-8 the change in speed is slightly smaller than the change in tangent velocity. (I drew a circle with the radius of the speed of v_I that...

Homework Statement An object is launched from the origin. At the peak of it's trajectory, it explodes into two fragments, one of mass m and the other of mass 3m. The smaller fragment of mass m lands back at the trajectory. How far from the origin does the second fragment land? Homework...

Hello, Granted that a body begins accelerating from rest with a constant acceleration a, and after a certain time T changes the direction of its acceleration and begins moving with acceleration -a, would it be correct to say that the body would return to its origin at time t=2T? I mean, are...

Can anyone solve this puzzle for me - a mass m in space with a constant velocity C heads toward a circular mass M such that if not disturbed it would pass by M at a distance of 2 of M's radiuses. However, the mass m experiences a second velocity Ve towards the center of M; the magnitude of this...

Hi guys! I had the following system of DE's to solve: \alpha '=-2i \alpha \beta ' =2i \beta. Where alpha and beta depend on t. I solved it by writing the system under matricial form, found the eigenvalues and corresponding eigenvectors. The solution is (and I've checked it, it works)...

Howdy folks, I have been given the opportunity to do some extra credit for my mechanics class. As an assignment, my prof would like to see a 3D trajectory plotted via a program (like Python). My basic assignment is to plot the trajectory of a soccer ball after it has been kicked. I don't...

Homework Statement For a lab that we did I need to draw the path of a horizontally fired projectile using a graph. When I look at the equation I derived it doesn't look like it will draw the path correctly. The Attempt at a Solution Δx = Vox*t T = Δx / Vox -h = Voy*t + .5*a*t2 -h =...

Hello, I have figured out the basics so far, but perhaps someone could help me figure out a bit more. I observed this meteorite moving across the sky, looking like a low airplane glowing bright bright orange. from the american meteor site (http://www.amsmeteors.org/fireballs/faqf/#1), this...

Homework Statement Okay, this is a projectile motion problem(No Drag) where a rock is thrown as 35m/s at an angle of 48 degrees. The question that I am struggling with is: "Find where and when the trajectory angle is 10 degrees?" Homework Equations The Equation that my teacher was used...

Hello Particle with nonzero mass moves on a curved trajectory. Why does it feel centrifugal gravity? Does spacetime curve or...? One answer might be that it feels gravity because the 1st law of Newton says so; but this wouldn't be good enough an answer :) Thank you

Homework Statement Find orthogonal trajectories for y=clnx, y=cex, y=sin(x)+cx Homework Equations Simple integration for the most part. The Attempt at a Solution I'm fairly confident on the first two, its the third that's giving me trouble. First, y=cln(x) c=\frac{y}{ln(x)}...

Homework Statement i Pmed some mentors but they said i should post it at forum, i asked Astronuc that if its ok to post this in forum and he told me to post it in this section.. i know some users here are very senior and surely have the knowledge to this and i want to learn. it is a...

Hello Forum, In kinematics we study motion and the trajectories of moving bodies. The trajectory is a line (straight or curved) that joins all the positions occupied by the object in the various instants of time. A trajectory has an equation that contains only spatial coordinates (not...

So I'm making a little basketball simulation game and I need a good way to calculate the path of a ball. I want to do this on a frame by frame basis where one frame lasts about 50 milliseconds. Each frame will store values for the state of the ball and then after applying some math, those values...

Homework Statement This is a problem about an aircraft flying above a cannon which is capable of firing in any direction. The plane's height, velocity and the speed of the projectile fired by the cannon are given (I am not trying to get help in solving the problem, so the numbers are not...

Hello everyone! I have calculated the velocities required for an orbiting body to follow a circular, parabolic, and hyperbolic trajectory around another massive body, which are the following: v_{circular} = \sqrt{\frac{\mu}{r}} = \sqrt{\frac{GM}{r}} v_{parabolic} =...

I am trying to predict the flight of an object with a parabolic trajectory including drag due to air resistance how do I do this? the wiki page was not clear its my understanding its relative to the square of the speed.

Hello All, This is my first post on any forum so I will try not to get too fancy. I have been writing in fortran for about two months now and it is my first programming experience. First, I wrote a classical dynamics program for a particle moving toward a potential barrier. Then, I wrote a...

Homework Statement So we launched small rockets on our last day, but have a week to turn in the homework based on the launch, but seeing as we aren't allowed back in school I can't ask questions I am lost. We haven't dealt with anything remotely related to trajectory since the beginning of...

It sounds like an easy-enough problem, but even writing down the ridiculously nonlinear equation that would need to be solved is making my face hurt. I'm talking classical/Newtonian gravitation, action-at-a-distance, constant-force. It could really be any external non-EM conserved force...

Hello, For something of a hobby of mine, I'm looking at different interplanetary trajectories for a Mars mission. I've got a somewhat interesting case; I only know basic calculus of a single variable (taken calculus 1), so I can't do the more in-depth multivariable and (I think) vector...

just thinking cross sections here. a neutron that is freed as a result of a fission of pure U235. travels @c/10(fast!) will its trajectory be perturbed by the gravitational force emitted by a nearby nucleus, or do things on the quantum level work differently?

In my class we have so far only dealt with electrostatics, i.e. fields of stationary charge distributions. However one question arose while doing so: Given a set of stationary source charges we can calculate the electric field at each point in space. But will that give us enough information to...

Hello. I am programming a 2d solar system simulation for a game. All went fine until I got to this part. Tried learning it in the past 3 days but could not understand most of it. Hoped to find help hhere. I have the location of both planets, their mass, their initial velocity and that's it. How...

Homework Statement There is a fixed spherical body of mass M whose center is to be taken as origin. Another body of mass m whose initial position vector \vec{r} is given. This body is projected with initial velocity \vec{v}. Find the equation of trajectory of body with mass m around the body...

Hello! I tried to develop equations of motion of system of wheels, where the first one with radius of r is rotated with some angular velocity v, the center of the second wheel is connected with the first on its perimeter and its plane of rotation is perpendicular to the plane of rotation of...

Hi, I use a numerical method to trace trajectories of particles. I want to program a sort of 'video' type graph. A graph or 3d video or perhaps just 3 graphs (xy, xz, and yz) that would show the position of the ion as the software is run. So my question is this... What software would...

Hi, I've got a problem here, that I'd like to discuss before trying to implement any sort of solution. Basically I've got a planetarium simulation, in which I'd like to plot a patched conic trajectory ahead of a spacecraft . The planetarium only simulates two-body gravity, and switches...

Homework Statement A ball is dropped from a height of 39.0m. The wind is blowing horizontally and imparts a constant acceleration of 1.20 m/s^2 to the ball. a. Show that the path of the ball is a straight line and find the values of R and θ (R is the distance on the x-axis from the ball's...

Homework Statement I want to be able to plot a trajectory wrt time of a ball that rolls without slip on a curved surface. Known variables: -radius/mass/moment of inertia of the ball. -formula for the curvature of the path (quadratic) -formula relating path length and corresponding height...

Homework Statement This a trajectory problem. A ball is launched from ground level at a unknown angle. ( ∅o= ? ) at an unknown velocity ( Vo = ? ) The ball travels 20 meters in the x direction and 25 meters up in the y direction. At this point (20,25) the ball hits a wall and a -45 angle...

Need to find the angle at which a plane should aim if when traveling at 210km/h with a 40km wind east produces a resultant angle of 60 degrees. I can write that 60=tan^-1(210sin60/(210cos60+40) and proceed from there: tan60=210sinx/(210cosx+40) 1.73=210sinx/210cosx+40...

I am a hack at this, so I am turning to you guys for help. I need to develop a mathematical model do generate the speed of a softball when struck with differing amounts of force. The specs are: weight of ball 188g applied force 170 lb to 500 lb The force is applied by a...

I would like to determine the equation describing the trajectory of an object using data from 2 distance sensors. I figured out how to do this if the sensors take simultaneous measurements but this cannot be done without generating crass talk between the sensors. The object moves too far when...