Projection Definition and 409 Threads

A golf ball with an initial speed of 91.1 m/s lands exactly 186 m downrange on a level course. The acceleration of gravity is 9.8 m/s2 . A)Neglecting air friction, what minimum pro- jection angle would achieve this result? Answer 6.35 minimum angle B)Neglecting air friction, what...

Homework Statement Hi, I got tied up with something.. I have a question that says if a projection P satisfies || P v || <= || v || then P is an orthogonal projection.. but if I drew in |R^2, a x-axis and a y=x line, and projected some vector onto the y = x line.. I still get || Pv || <=...

Homework Statement A person starts at coordinates (-2, 3) and arrived at coordinates (0, 6). If he began walking in the direction of the vector v=3i+2j and changes direction only once, when he turns at a right angle, what are the coordinates of the point where he makes the turn. Homework...

I am computing a stereographic projection in R^4 and i think i am correct in setting x=rcos(x)sin(y) y=rsin(x)sin(y) z=rcos(y) but can't see how to compute r as I do not know to visualise it graphically as was possible in R^3, any help would be greatly appreciated

I need to find the components of the force along AB along AC. So I got unit vectors for each like so: \vec{AB}=<-1.5,-3,1> \vec{AC}=<-1.5,-3,3> Norm AB=sqrt(12.25). Norm AC=sqrt(20.25). Then after multiplying the unit vector AB by the force I tried using the vector projection...

Homework Statement hello, I need help with projection of a rigid body with moment of inertia I, the rigid body was earlier moving on a circle of R radius with \omega angular velocity and was making angle of \alpha when centripetal force stopped to work. And I need to know if this rigid body...

The Projv(x) = A(ATA)-1ATx I'm puzzled why this equation doesn't reduce to Projv(x) = IIx since (ATA)-1 = A-1(AT)-1 so that should mean that A(ATA)-1AT = AA-1(AT)-1AT = II What is wrong with my reasoning? Thanks.

Hello, if we consider the stereographic projection \mathcal{S}^2\rightarrow \mathbb{R}^2 given in the form: (X,Y) = \left( \frac{x}{1-z} , \frac{y}{1-z} \right) how can I find the metric in X,Y coordinates? -- Should I first express the projection in spherical coordinates, then find...

Hello, Is there such a thing as a projection screen that is transparent to IR? I need to project an image onto a screen (rear-projection), but I also need to send an IR signal through the screen from the side of the human user back to the side with the projector. I think there are...

Homework Statement Show that the map f : R--> S1 given by f(t) =[(t^2-1)/(t^2+1), 2t/(t^2+1)] is a homeomorphism onto S1-{(1, 0)}, where S1 is the unit circle in the plane. I know this is a stereographic projection, but I do not know how to show that it has a continuous inverse. I am...

I want a projection of Earth where distances are undistorted. i.e. 10 degrees of latitude at the equator is exactly the same map distance as 10 degrees of latitude at the Arctic Circle. As a disqualified example, the Mercator Projection has map distance increasing with increasing latitude...

Hi guys, I recently read some stuff about satellites in space being able to project 3D images on to the sodium layer of our atmosphere about 60 miles above the Earth. Is this possible? Can the sodium layer potentially be used as a giant movie screen for projections? The stuff i read was about...

1. Homework Statement The speed of projectile when it reaches its maximum height is one it half speed when it’s half maximum height. What is initial projection angle of the projectile? 2. Homework Equations I know it has been asked several times but no one give the answer with...

Hey PhysicsForums. Long time reader looking for some assistance Homework Statement [PLAIN]http://img205.imageshack.us/img205/3923/physicsg.jpg 2. The attempt at a solution I'm pretty sure the idea is to find the unit position vector to point A, and the force vector F. I found...

Homework Statement Find the scalar and vector projection of the vector b=(3,5,3) onto the vector a=(0,1,-5) . Homework Equations The Attempt at a Solution What I've tried is multiplying all the i's and j's and k's together and adding up everything because you get a scalar...

Homework Statement If a = <3,0,-1> find the vector b such that compaB = 2 Homework Equations None. The Attempt at a Solution |a| =\sqrt{3^2 + 1^2} = \sqrt{10} compaB = \frac{ a\cdot b}{|a|} 2 = \frac{3(b1) - 1(b3)}{\sqrt{10}} 2\sqrt{10} = 3(b1) - 1(b3) I don't know...

For a game I am thinking about making I would need to know how to project points from a differentiable bounded 3-manifold to a Euclidean plane (the computer screen). The manifold would be made from a 3-dimensional space with two balls cut out of it and a hypercylinder glued onto it at the holes...

Hi, Suppose I have a space X with coordinates (x,y,z) and a space Y with coordinates (x,y,z,t), so that dim(Y)=dim(X)+1. What is the difference between the projection (x,y,z,t)->(x,y,z) and the inclusion (x,y,z)->(x,y,z,t)? Are they each others inverses? Especially if x=x(t), y=y(t) and...

I see lots of references to time being the fourth dimension as well as there being 3 + 1 dimensions to spacetime as we know it, etc. I also see that time has to be treated differently in some of the constructs of physics. So it seems that time seems to be both similar and dissimilar to the other...

So basically I want to write some code in Python to project the movement of the moon and sun across the night sky. Basically, I need a projection such that the shape of the moon won't change as it moves in the sky (especially when it's near the horizon) - the objects have to look fairly good...

Hey, I have a linear algebra exam tomorrow and am finding it hard to figure out how to calculate an orthogonal projection onto a subspace. Here is the actual question type i am stuck on: I have spent ages searching the depths of google and other such places for a solution but with no...

Homework Statement triangle in the plane z=1/2y with vertices (2,0,0) (0,2,1) (0,0,0) please help me to find out the projection of the triangle in xy plane. thanks Homework Equations The Attempt at a Solution

Homework Statement That is the question. The answer on the bottom is incorrect Homework Equations I believe that is the formula that is supposed to be used. The Attempt at a Solution All I really did was plug in the equation into the formula but there is something I am...

Hey, here is the formal question. M is a riemannian sub-manifold in N. a,b are vector fields such that for each p\inM, ap,bp \in TpM \subset TpN prove \nablaMba = pr(\nablaNba) where pr is the projection funtion pr:TpN\rightarrowTpM and \nablaN and \nablaM are the covariant derivative...

hi, so this is actually for a program I'm writing, but it's definitely more of a math question than a programming question. basically, i have an object that gets detected by a webcam attached to a computer. the object is just a piece of paper with a pattern on it, so it is, for the purpose of...

Suppose I had a plane and for whatever reason, I chose two non-orthogonal vectors in R3 to define that plane (they define a basis for the plane?). Suppose I have another vector in that plane. How do I find the (contravariant?) coordinates of another arbitrary vector in that plane? All I want...

Homework Statement So we have an observable K = \begin{bmatrix} 0 & -i \\ -i & 0 \end{bmatrix} and its eigenvectors are v1 = (-i, 1)T and v2 = (i, 1)T corresponding to eigenvalues 1 and -1, respectively. Now if we take the outer products, we get these... |1><1| = (-i, 1)T*(i, 1) =...

I was just wondering where or if the brain projects mental pictures. I see them in front of my forehead. Is there where everyone sees them or is it different for everyone?

Homework Statement Prove that [P]^2=[P] (that the matrix is idempotent) Homework Equations The Attempt at a Solution A(A^T*A)^-1 A^T= (A(A^T*A)^-1 A^T)^2 Where A^T is the transpose of A. I have no idea.

Let S be a subspace of R3 spanned by u2=\left[ \begin{array} {c} \frac{2}{3} \\ \frac{2}{3} \\ \frac{1}{3} \end{array} \right] and u3=\left[ \begin{array} {c} \frac{1}{\sqrt{2}} \\ \frac{-1}{\sqrt{2}} \\ 0 \end{array} \right]. Let x=\left[ \begin{array} {c} 1 \\ 2 \\ 2 \end{array} \right]...

Hi everybody, Guys I'm a total stranger to physics. I need some help to find the relationship between the major/minor axes of an ellipse and the radius of a sphere in a cone of light. For example, imagine a light source is located at 'h' height from a plane and a sphere(with a radius of...

I'm an undergraduate computer-science student doing research in the field of computer vision, and one of the tasks I've been charged with is calibrating the camera on a robot. I understand the basic principles at work: a vector in 3D world coordinates is transformed into homogeneous 2-space...

Hi, in questions involving lenses, when using the "thin lens formulae" if my di is negative doesn't that mean the image is on the other side of the lens? in this example however it doesn't seem this holds true.. A doctor examines a patient's skin lesion with a 15 cm focal length...

D(g) is a representaiton of a group denoted by g. The representaion is recucible if it has an invariant subspace, which means that the action of any D(g) on any vector in the subspace is still in the subspace. In terms of a projection operator P onto the subspace this condition can be written...

This is from my Vector Analysis course today. We've been doing a bit of abstract stuff since class began, but the professor said we're going to get to concrete stuff pretty quickly. I think the notation is throwing me off a bit. I'm not sure why the alphas change for each successive...

on U, where U = span{(1, -1, 1, -1), (2, 0, -3, 1)}

This problem refers specifically to http://books.google.com/books?id=W9ZuLZWldUoC&lpg=PA9&ots=2lrfqlB3j7&dq=%22stress%20components%20on%20an%20arbitrary%20plane%22&pg=PA10#v=onepage&q=%22stress%20components%20on%20an%20arbitrary%20plane%22&f=false". The text comments that Area BOC =...

Sorry 'bout posting so many topics but there are too many things that are unclear to me. CMBR measurements suggest the universe is pretty much FLAT, but I don't see it as flat, and forget our planet, all those vast spaces in every spatial dimension - all that is flat? It obviously has depth...

Hello everyone, If I have a collection of data points (vectors), and x and y are two vectors among them. I want to project the data to a direction that the Euclidean distance between x and y is Maximally preserved. Then this direction should be the row space of (x-y)’, denoted as row( (x-y)’...

Homework Statement Well, I was trying to find an equation that would let me calculate what angle I have to put my gun at to get the projectile to hit a specified distance. Not actual homework, but something I'm trying to do for a game (Garry's mod) So the initial velocity of the shell...

I was reading Lie Algebras in Physics by Georgi......second edition... Theorem 1.2: He proves that every finite group is completely reducible. He takes PD(g)P=D(g)P ..takes adjoint...and gets.. P{D(g)}{\dagger} P=P {D(g)}{\dagger} So..does this mean that the projection...

edit: This thread might need moved, sorry about that. Hi, I have ended up on this site a few times after searching various maths issues; it seems to have a good community so I am asking you good people for a little help understanding this. Tomorrow I have a semi-important maths exam, if I fail...

[b] Def1. Let L be a line in E. We define the "orthogonal projection onto L" to be Ol = {(P,Q)| P,Q in E and either 1.P lies on L and P=Q or 2.Q is the foot of the perpendicular to L through P. Problem 1. Let L be a line in E. Show that Ol is not a rigid motion because it fails...

Let A be a matrix corresponding to projection in 2 dimensions onto the line generated by a vector v. A) lambda = −1 is an eigenvalue for A B) The vector v is an eigenvector for A corresponding to the eigenvalue lambda = −1. C) lambda = 0 is an eigenvalue for A D) Any vector w perpendicular to...

I was reading about a certain methood that uses projection to calculate the probability of finding a particle in a certain state. The explanation is not detailed enough for me to get my head around how to use it, but maybe some of you people are familiar with the methood? The methood goes like...

Homework Statement A ball was projected at an angle A to the horizontal. One second later another ball was projected from the same point at an angle B to the horizontal. One second after the second ball was released, the two balls collided. Find the speed of projection for the two balls...

Homework Statement Determine the matrix for the spatial projection perpendicular to the straight line (x1, x2, x3) = t(1, 2, 3). The vector space is orthonormal. Homework Equations The Attempt at a Solution After a trip to #math on freenode that resulted in discussions of Gram-Schmidt...

Quantum - Projection Probability - "Projection amplitudes for SHO states." Given the two normalized 2D SHO wave functions <x,y|mx[/SUB ],ny> for the second energy level n = nx + ny = 1 in the m[SUB]x[/SUB ],n[SUB]y representation: <x,y|1,0> = (2/pi)1/2xexp[-(x2+y2)/2] <x,y|0,1> =...

Homework Statement Give an example of a subspace W of a vector space V such that there are two projections on W along two distinct subspaces. Homework Equations The Attempt at a Solution I tried looking into Euclidean geometry spaces (R3 and R2) but no matter what subspace W I...

Homework Statement curve S is the intersections of two surfaces, i have to find the curve obtained as the orthogonal projection of the curve S in the yz-planeHomework Equations how do i find the orthogonal projection of curve S??The Attempt at a Solution i found the equation of curve S to be...