Plane Definition and 1000 Threads

Homework Statement Find th distance of point P to the plane OQR, O being the origin. "PS" is perpendicular to plane "OQR" P(3,-2,-1) S(x,y,z) O(0,0,0) Q(1,3,4) R(2,1,-2) Homework Equations A) The equation in terms of (x,y,z) obtain by triple product of OS,OQ & OR. OS.(OQXOR)=0... [all being...

I have a circle with centre (-4,0) and radius 1. I need to draw the image of this object under the following mappings: a) w=e^(ipi)z b) w = 2z c) w = 2e^(ipi)z d) w = z + 2 + 2i I have managed to complete the question for a square and a rectangle as the points are easy to map as they are...

Homework Statement Two objects of 2.8kg and 4.2kg are connected by an inextensible cord. The object's at rest on a plane inclined 22°, determine the object's acceleration and tension in the cord if a 60N force is used to push the object downward. Homework Equations ΣFnet = ma the plane is...

Sorry if this has been answered already, i searched for a while. I know how to solve the problem of the potential of a point charge near a grounded infinite conducting plane, and a line charge near an infinite conducting plane. If the plane isn't necessarily grounded, say its at some potential...

edit: fixed typo's andrewkirk pointed out, oops I can cover the projective plane with 2 open sets U,V where each of these neighborhood contains the point that is missing, and the intersection of these two neighborhoods will be simply connected. I was then hoping to invoke the Seifert-Van-Kampen...

Question: Starting from rest, the toy plane flies around a circle of radius 2m, three times in 3 seconds. There is constant tangential acceleration, fins the magnitude of the acceleration at the end of 0.5s. My solution (most likely wrong): Circumference= 2pir= 4pi= 12.56631 Distance...

$\textsf{write an equation for}$ $\textsf{ The plane through the point (3, 2, -5) and perpendicular to the x-axis}$ 4ok I know this goes thru $3$ on the axis and it is \parallel to the $yz$ plane so is it just $x=3$.

Homework Statement I'm asked to show that the two dimensional plane wave (for constant C) \psi \left ( \mathbf{r} \right )=Ce^{-i\mathbf{k}\cdot \mathbf{r}} satisfies the Schrödinger equation: -\frac{\hbar^{2}}{2m_e}\frac{\mathrm{d}^2 \psi\left ( \mathbf{r} \right )}{\mathrm{d}...

The Euler Characterist of the projective plane and sphere is given by V - E + F. V is vertices, E is edges, F is faces. A presentation of the projective plane is {a | aa} and a presentation of the sphere is {b | bb^1} Yet the Euler characteristic is 2 for the sphere and 2-n for the connected...

I am reading Bruce P. Palka's book: An Introduction to Complex Function Theory ... I am focused on Chapter 2: The Rudiments of Plane Topology ... I need help with an aspect of Theorem 1.8 ... Theorem 1.8 (preceded by its "proof") reads as follows...

$\textsf{Write a complete solution.}\\$ $\textit{Let}$ $$v =\langle 1, 3, − 1 \rangle$$ $\textit{and }$ $$r_0 =\langle 1, 1, 1 \rangle$$ $\textit{and consider the line given by:}\\$ $$r = r_0+tv$$ $\textit{in vector form.}\\$ $\textit{Also, consider the plane given by}$ $$x+2y+2z+2 = 0$$...

For finding the critical speed or the minimum speed in a question for a vertical plane, you take either the friction or the contact (normal) force to be 0, so F=W However, for a horizontal plane, like spinning something around in a circle, you can still do F=W to find the critical speed or the...

Homework Statement Homework Equations https://answers.yahoo.com/question/index?qid=20120204205204AAEvo8V The Attempt at a Solution This is my attempt following the solution in the yahoo answer, yet it is incorrect... Can anyone tell me if I have made mistake in any of the manipulation? Any...

$\textsf{Find the vector perpendicular to the plane PQR determined by the points}$ \begin{align*}\displaystyle &P(2,1,3), \, Q(1,1,2), \, R(2,2,1)\\ \end{align*} $$\textbf{ solution:}$$ \begin{align*}\displaystyle \vec{PQ}&=(1-2)i+(1-1)J+(2-3)k=&-i-k\\...

So this is the problem: A 250-kg crate is on a rough ramp, inclined at 30° above the horizontal. The coefficient of kinetic friction between the crate and ramp is 0.22. A horizontal force of 5000 N is applied to the crate, pushing it up the ramp. What is the acceleration of the crate? Relevant...

Homework Statement In the figure below, a radar station detects an airplane approaching directly from the east. At first observation, the range to the plane is d1 = 412 m at 40° above the horizon. The airplane is tracked for another 123° in the vertical east–west plane, the range at final...

Could someone please provide a diagram of all the forces acting on the plane, and explain why the answer is E? This is from the 2014 F=MA exam. Thanks, blueblast

Dear Everybody, What force (in N) must be applied to a 150.0 kg crate on a frictionless plane inclined at 30° to cause an acceleration of 7.1 m/s2 up the plane? Work: I know the sum of the force in the x direction must be equal to mass multiply by acceralation.Thanks Carter

Homework Statement Cylinder : x^2 + y^2 = 1 Plane that intersects above cylinder: y + z = 2 What is the surface area of the sides of this cylinder? Homework Equations dS= R1 d@ dz @ is from 0 to 2 pi z is from 0 to 2 - y dS=(Zx^2 + Zy^2 + 1)^.5 dA Where Z = 2 - yThe Attempt at a Solution I...

Hi, I wonder if we place a camera at any secondary lobe in a double slits fringe pattern, and if it looks at the slits: where does the light come from, how is it distributed ? And if we zoom inside one of the slits, what does it look like ? Subsidiary problem : in the diffraction pattern...

Homework Statement A ball falls on an inclined plane of inclination theta from a height h above the point of impact and makes a perfectly elastic collision. Where will it hit the plane again ? Solve the previous problem if the coefficient of restitution is e. Use theta = 45°, e = .75 and h =...

Homework Statement [/B] A block of mass m rests on an inclined plane with angle o accelerating to the right with acceleration a. The coefficient of static friction is u.Homework Equations For what range of a does the block remain at rest on the plane. The Attempt at a Solution [/B] I started...

Homework Statement 13.24 A particle travels along a plane curve. At a certain instant, the polar components of the velocity and acceleration are vR=90mm/s, vθ=60mm/s, aR=-50mm/s2, and aθ=20mm/s2. Determine the component of acceleration that is tangent to the path of the particle at this...

Hey! :o A differentiable function $f(x,y,z)$ has $\nabla f (x_0, y_0, z_0) \neq (0,0,0)$ and zero instant rate of change from $(x_0, y_0, z_0)$ in the direction $\left( \frac{2}{3},-\frac{1}{3},-\frac{2}{3}\right)$. Which could be the cartesian equation of the tangent plane of the level surface...

I made a few paper airplanes. I noticed that the common paper airplane (shown below) https://i.ytimg.com/vi/v29M7Oa1l-A/hqdefault.jpg flies much further/better than paper planes that look like standard 747s. Any know why ? I expected 747 like plane to be very efficient at generating the lift...

Homework Statement We have an inclined plane with a mass ##M## and an angle ##\alpha## and a box of mass ##m## over it. Everything is at the instant 0 (it's a problem of static, no dynamics). a) What's the acceleration in the component x of the box? b) What's the acceleration in the component y...

Homework Statement Give examples of maps between subsets of the plane (with Euclidean toplogy) that are: a) open but not closed or continuous b) closed but not open or continuous c) continuous and open but not closed e) continuous and closed but not open f) open and closed but not continuous...

Homework Statement A pilot flies a plane from A to B, 400 miles due North of A. If a Westward wind of ##20 mph## is present, determine the direction the pilot needs to aim the plane relative to the air and the speed at which he needs to fly the plane in order to arrive at B in two hours...

A particle moves in a vertical plane from rest under the influence of gravity and a force perpendicular to and proportional to its velocity. Obtain the equation of the trajectory, and identify the curve.

<Moderator's note: Moved from a technical forum and therefore no template.> I don't understand the math here which is troubling considering I got A's in calc 2 and 3... I tried to divide both sides by cos(theta) and solve for tantheta. but that gives something different. Also, what does...

Good afternoon! Please help me figure out the mathematics of this simple plane wave question! 1. Homework Statement 2. Homework Equations n1*sin(theta1)=n2*sin(theta2) The Attempt at a Solution I need help calculating the angle of incidence. I found the propagation vector for incidence...

1. The problem statement, all variables, and given/known data A block with an initial speed of 20.0m/s slides up a ramp with an incline angle of 30º. (a) (2 points) Write the position as a function of time for motion up the surface of the ramp. (b) (2 points) Write the velocity as a function...

Homework Statement A truck of mass 1.5 tonnes (1500 kg) is moving at a speed of 36 km/h down a hill of slope 1 in 6. The driver applies the breaks and the truck comes to rest after 2 seconds. Find the breaking force, which is assumed to be constant, ignoring any other resistant forces...

Homework Statement Homework EquationsThe Attempt at a Solution I'm not sure how to even begin this problem. My notes mentioned something about a Mobius Transformation but that's not something that I've been taught, and certainly not something I'm familiar with. Any advice would be greatly...

Imagine a 747 sitting on a large conveyor belt, as long and as wide as the runway. The conveyor best is designed to exactly match the speed of the wheels, but run in the opposite direction. CAN THE PLANE TAKE OFF?

How is it possible to ignore the addition sign and imaginary number without contradicting fundamental Mathematics? I find it difficult to understand.

Not sure if I'm doing this right would love input Consider a box m=50kg which is being pulled on a rough, horizontal surface by a person using a rope . Assume that the person is applying a force of T=150N on the block , the rope makes an angle of 30 degrees with the horizontal and the...

Homework Statement Homework Equations 3. The Attempt at a Solution [/B] I have drawn this diagram using MS paint, could you please tell me some other software in which I can draw and insert greek symbols, too ?Let me take the origin at O. ## \hat r \left(\alpha\right) ≡ \hat r\text{ at...

Homework Statement A very thin, finite, and uniformly charged line of length 10 m carries a charge of 10 µC/m. Calculate the electric field intensity in a plane bisecting the line at ρ = 5 m. Homework EquationsThe Attempt at a Solution Not sure why I'm not getiting this but I've been at this...

I googled and found this angle of Earth is claimed to be 1.5787 degree. Does it change over the time? Does anyone know any history of this tilt? I wonder if it's linked to global warming.

Homework Statement An Airbus 380 needs to reach the velocity of 280 kmh^-1 before it takes off. The maximum acceleration the plain reaches in the runway is 0.95 ms^-2. Verify THAT the plane can use an airport with this runways. Runway 1: 3805 meters (SSW-NNE) Runway 2: 2400 meters (S-N)...

Hello all, I wish to plot and following complex numbers on a plane, and to find out which shape will be created. I find it hard to figure out the first one, I believe that the others will follow more easily (the forth is also tricky). \[z_{1}=\frac{2}{i-1}\] \[z_{2}=-\bar{z_{1}}\]...

Homework Statement Homework Equations I want to know whether my process is correct? THANKS! The Attempt at a Solution [/B] 1. By using Gauss's law: E\cdot 2\pi rz = \frac{\lambda z}{\epsilon_{0}}\Rightarrow E=\frac{\lambda}{2\pi\epsilon_{0} r} In my coordinate system...

Homework Statement the plane C is being tracked by radar stations A and B. At the instant shown, the triangle ABC lies in the vertical plane, and the radar readings are θA=30o, θB = 22o, θA(dot) = 0.026rad/s and θΒ(dot) = 0.032rad/s. Determine (a) the altitude y; (b) the speed v; and (c) the...

Homework Statement A capacitor with C is charged by a battery to a voltage V and then disconnected. The distance between plates is slowly increased by an external force. What is the change of the electrostatic energy of capacitor during this process? Homework Equations I have two ways to solve...

hey So Fourrier transform is ##f(t) = \frac{1}{2 \pi} \int_{-\infty}^{\infty} F(\omega) e^{i \omega t} d\omega## with ##F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i \omega t} dt## Question 1 - The Fourier mode for the continuous case is ## \frac{1}{2 \pi} F(\omega) e^{i \omega t}##, is...

Hi all, I am working on a rubber band plane (something like this: http://www.instructables.com/id/Rubber-Band-Powered-Aeroplane/) and I got a question regarding to the physics on these plane. As there is only one propeller and one rubber band, when the rubber band untwist, why doesn’t it rotate...

A ball, which can be regarded as pointin all its effects, falls steady , subject only to the weight force, on an inclined plane of an angle α with respect to the horizontal from a height h computed from the impact point. The ball bounces elastically. Get the d height can reach the ball and the...

Hi! If a holomorphic function ##f:G \to C##, where ##G## is a region in the complex plane is equal to zero for all values ##z## in a disk ##D_{[z_0,r]}##, inside ##G##, is it zero everywhere in the region G? And if this is true, does it mean that if an entire function is zero in a disk, it is...

Interesting new jet plane has rolled out of its hanger. https://img.purch.com/h/1400/aHR0cDovL3d3dy5zcGFjZS5jb20vaW1hZ2VzL2kvMDAwLzA2Ni80NjMvb3JpZ2luYWwvZHJvbmUxX3dlYnNpdGUuanBnPzE0OTYyNjgyNTY= It looks like there are vibration modes of the plane that during normal operation would shake the...