Angle Definition and 1000 Threads

Homework Statement Find the angle of inclination of a line when the slope, m, is equal to -1/2 Homework Equations m = rise/run = tan(φ) φ=angle of inclination The Attempt at a Solution I thought the answer would simply be using arctan on the slope, but my answer gives me -26.565051 degrees...

I was curious, if you were given a vector field F(x,y,z) = <Fx(x,y,z), Fy(x,y,z), Fz(x,y,z)>, and then some scalar function f(x,y,z), how would you define a function θ(x,y,z) of the angle θ between the scalar function and the vector field at any given point. I know how I would find this at a...

Hi All. Given a 20 inch L bar with 1" sides. If 6 inches of this bar is buried in a concrete wall horizontally, which orientation would render the most downward force strength? 1. A V orientation with the tip of the V pointing down. 2. A V orientation with the tip of the V pointing up. 3...

Is there any way to design a lens or system of lenses where I see the same part of the image, irrespective of direction or angle of view. The light rays can be assumed to be collimated as viewing will be from a distance. Actually- I am looking at focusing on a point or specific area of the...

Homework Statement Find the slope of the tangent line to the give polar curve at the point specified by the value of theta R = 1/θ, θ=π Homework Equations ##\frac{(dr/dθ)sinθ + rcosθ}{(dr/dθ)cosθ - rsinθ}##The Attempt at a Solution The derivative of r is -1/θ2 Then plugging things into the...

$\triangle ABC,\angle B=30^o , \,\,and \,\, \overline{BC}^2 - \overline{AB}^2=\overline{AB}\times \overline{AC}\\ find \,\, \angle C=?$

Homework Statement Find the angle between the straight lines: ##(x^2+y^2)(\cos^2{\theta} \sin^2{\alpha} + \sin^2{\theta})=(x \tan{\theta} - y \sin{\alpha})^2## Homework Equations [Not applicable] The Attempt at a Solution Dividing by ##x^2##, ## (1+(\frac{y}{x})^2)(\cos^2{\theta}...

Homework Statement I'm working on a project right now, which uses laser beams and part of the project requires me to find a mathematical model which relates angle of projection to the intensity of the light. Does anyone know of an equation(s) which relates the intensity and angle together...

Homework Statement A cyclist is initially heading exactly due North. He then initiates a turn to the West, the turn being a quarter circle with radius 12-m. He travels at a constant speed of 5.5-m/s during the turn. What is the direction of this average acceleration, measured anti-clockwise...

Homework Statement Light of a wavelength 548nm illuminates two slits separated by 0.25mm. At what angle would one find the phase difference between the waves from two slits to be 2 rads? Homework Equations σ / λ = ΔΦ / 2π σ: path difference λ: wavelength Δφ: phase difference The Attempt at a...

Simple geometry can compute the height of an object from the object's shadow length and shadow angle using the formula: tan(angleElevation) = treeHeight / shadowLength. Given the shadow length and angle of elevation, compute the tree height. #include <iostream> #include <cmath> using namespace...

Homework Statement See photo attachment Homework EquationsThe Attempt at a Solution Ive begun by defining an x and y axis, followed by find the sum of x-components of the forces, and y-components. Followed by the magnitude of the resultant force. The only method i could think of was to find...

Hey! :o If a particle of mass $m$ has velocity $v$, its momentum is $p=mv$. In a game with balls, one ball of mass $2g$ springs with velocity $2m/s$, it hits two balls, both of which have mass $1g$, and stops. The one ball get soared with velocity $3m/s$ and with angle $45^{\circ}$ to the...

Homework Statement I have 3 masses (Fα, Fβ & Fg) with 2 pulleys, and a wind variable which is in static equilibrium. I have already calculated the appropriate forces for the 3 masses by multiplying it with 9.81m/s² (gravity). Fwind = 60N Fα = 313.9N Fβ = 619N Fg = 882.9N I'm required to find...

Homework Statement http://loncapa.vcu.edu/res/vcu/phys202/zzImages/Ch25_TB.jpg A charged ball with charge Q1 = 0.1 μC and mass 0.05 kg is suspended from a ceiling with a thin massless string as shown in the figure. The second charged ball has a net charge Q2 = -0.5 μC and it is located d = 0.3...

In addition, why is there no magnetic field along the line of motion of a charge? If length contraction occurs along this line of motion, I don't see why there is no magnetic field created along this line of motion for other charges to interact to. I get magnetism is fundamental, but at least...

Homework Statement "Find the tension in the right string, when the left string is cut, if the mass of the rod is ##m## and its length is ##l##, and ##\sin \theta = 3/5##. The rod is initially horizontal." Please refer the diagram below (sorry for its clumsiness!). Homework Equations $$I_{rod}...

Hello! (Wave) A ship that is at the position $(1,0)$ of a chart ( with the north at the positive direction $y$) "sees" a rock at the position $(2,4)$. Which is the vector that connects the ship with the rock? What angle $\theta$ does this vector form with the direction of the north? I have...

Homework Statement Ball strikes inclined plane of infinite mass with velocity v vertically. Elastic collisions. Velocity and direction after collision? One way of solving is take components along and perpendicular to inclined plane and then solve easily. Is there any way to solve is using...

Hey guys, I'm having difficulty with my university project which is to build an electric bike. My design is to have a friction wheel attached to the shaft of my 800W 2800rpm electric motor which is rated at 2.8Nm. I have two issues with my spreadsheets at the moment. Can someone please help...

Could anyone please tell me how to get this answer through calculations and other means?

Hi. I'm a computer science student developing a kalman filter for autonomous sailboat, but I severely lack knowledge of the physics behind sailboats. I have a wind sensor giving data about wind speed and wind velocity, problem is the data is unreliable. So i thought that i could estimate what...

In ultrasound what is the difference between beam steering angle and Doppler angle thanks

I'm curious if it looks like I defined the reasons correctly to prove that FBCD is indeed a parallelogram. Specifically, I'm unsure if I'm using #4 "definition of coincident" and #5,6 "reflexive property" correctly in their terminology. I don't have anyone else, or any teacher to ping this...

Homework Statement You have a device that shoots an object at an angle, on top of a desk. You have x,y and v solve for the angle. Origin is at the top of the desk. Homework Equations y=vyot+(½)ayt2 x = vxot vsinΘ = vyo vcosΘ = vxo The Attempt at a Solution y= vsinΘt + (1/2)at^2 x = vcosΘt →...

Homework Statement Mass ##M## hangs from a string of length ##l## which is attached to a rod rotating at constant angular frequency ##\omega##. The mass moves with a steady speed in a circular path of constant radius. Find ##\alpha##, the angle the string makes with the vertical. Homework...

why light can't penetrate the prism with 45 degree angle?

Homework Statement Charges 2q and -q are located on the x-axis at x=0 and x=a respectively. (a) Find the point on the x-axis where the electric field is zero, and make a rough sketch of some field lines. (b) You should find that some of the field lines that start on the 2q charge end up on...

I'm building a clothing rack that swings out of the way. It's ideally made of 7/8" (or possibly 1") stainless steel tube, with 1/16" thickness and will sit on a 3" bearing (lazy susan) that supports 200lb. The top is firmly attached to a stud in the sloped ceiling. It needs to hold up something...

Here is the problem verbatim: The polar and azimuthal angles of a vector are Θ1 and Φ1. The polar and azimuthal angles of a second vector are Θ2 and Φ2. Show that the angle ϒ between the two vectors satisfies the relation: cos ϒ = cosΘ1*cos Θ2+sinΘ1*sinΘ2*cos(Φ1-Φ2) Hint: write out the...

Homework Statement Homework Equations ## θ_{brewster} = arctan(\frac{n_2}{n_1}) ## The Attempt at a Solution Hi all I'm having difficulty on this part of a question Now, showing that all light passes through is to say that there be no reflection. This occurs when the angle of incidence...

Homework Statement A block of mass m slides down a frictionless ramp from height h above the floor. At the base of the ramp it collides and sticks to the lower end of a uniform rod, length L, mass 2m, that is suspended about a pivot at point O, about which it is free to rotate. Express...

Homework Statement Homework EquationsThe Attempt at a Solution Using parallel lines I got the angle as theta.

Homework Statement Show that vector C = (BA + AB) / (A + B) is an angle bisector of A and B. Where vectors are represented by bold font, and magnitudes are regular font. Homework Equations A ⋅ C = A C cos(θ) ⇒ cos(θ) = (A ⋅ C) / (A C) B ⋅ C = B C cos(θ) ⇒ cos(θ) = (B ⋅ C) / (B C)The...

Homework Statement I have to do a high school report investigating the relationship between the angle of descent and the velocity of a ball rolling across a horizontal surface after it has gone through a ramp. I have collected the data already with the use of photo gates that measured the...

Hello, I am wondering about the following action in a stator: If the inlet angle in a stator is B, and the outlet angle is -B, what exactly is happening? Axial vlocity should be constant, and so should the relative velocities except being mirrored and i am asuming infinitely thin blades.. Can...

Hello! In this previous post, most replies point out that it is not possible to predict the angle of refraction (and so the frequency) at a certain interface, given the wavelength of the original signal. In particular, But when dealing with optical waveguides, it seems to be different. I am...

Homework Statement If a vector makes 45 degrees and 60 degrees with x-axis and y-axis respectively then the angle it makes with z-axis is equal to Homework EquationsThe Attempt at a Solution

Homework Statement Homework Equations ΣFx=max The Attempt at a Solution I drew a free body diagram for the box and set up the equation to solve for θ, but I'm not sure how to do it without μ

Homework Statement 2 parallel plates of length 4.0 cm are arranged horizontally in a vacuum. The upper plate is positively charged and the lower plate is negatively charged. An electron is projected horizontally with an initial velocity of 6.0 x 106 ms-1 and experiences a constant electric...

I recently came across an equation stating that ## \lambda_{ob} = \frac{\lambda}{cos(\alpha)} ## if ##\alpha## is the angle the observer is relative to the wave's direction of propagation. I guess I can kind of understand that a person perpendicular (i.e. ##\alpha = 1##) would see the normal...

OK I'm about to grow (more) gray hairs... Could some friendly soul smarter than myself kindly help me solve for both f and theta respectively in the following equation, please: x = sin[ (pi*f*W)/c * sin(theta) ] / [ (pi*f*W)/c * sin(theta) ] Getting stuck at "arcsin of arcsin" sort of...

Homework Statement A ski jumper leaves the ski track moving in the horizontal direction with a speed of 25.0 m/s as shown in Figure 4.14. The landing incline below her falls off with a slope of 35.0°. Where does she land on the incline? I've attached an image of the problem, my work is below...

Homework Statement When completing this problem I am able to find a value for the phase angle but am unsure of how to find the quadrant for the phase angle therefore unable to get the correct phase angle. Homework Equations Provided in the question: x = xmcos(wt+ phi) The Attempt at a...

Homework Statement Hi! I need to find the opening angle of the loss cone at a given altitude, when the magnetic latitude is 65 deg. Homework Equations See below The Attempt at a Solution First, I used the following equation to calculate the magnetic field at a given altitude...

Homework Statement You have a geostationary satellite (location 0◦N 0◦E, 36000 km above geoid). Assume the Earth to be spherical with a radius of REarth = 6372km When observing a region centered at 60◦N 0◦E: What is the incidence angle of the satellite’s line of sight (at pixel center...

Circulation of a magnetic field = closed loop integral ∫c B ⋅dl = μ0I B is mag field strength, dl is small line element, I is current Im imagining both B and dl point in the same direction from the diagram. So the dot product here, I picture as cosθ = cos0 Is that correct way to...

Homework Statement At midnight (local time) on Dec 21st 2015, the Local Sidereal Time at Palomar Observatory, California, was 6h 27m. Palomar Observatory has latitude 33◦ 210 2100 N, and longitude 116deg 51arcmin 60arcsecW. a) What was the approximate Local Hour Angle of the Sun at 23:00 local...

Homework Statement Four identical balls are thrown from the top of a cliff, each with the same speed. The first is thrown straight up, the second is thrown at 30° above the horizontal, the third at 30° below he horizontal, and the fourth straight down. How do the speeds and kinetic energies of...

If I have an electric field between a cathode and an anode, are there electric field lines between the plates? If yes, what happens if a charged particle enters the field at an angle? Is the force acting on the particle reduced?