Angle Definition and 1000 Threads

I tried to use complementary angles and the law of reflection but I still have no idea how to find the angle.

I understand how the diagram below determined the ##x## and ##y## axis for the velocity vectors but I don't understand the gravity vectors. What I don't understand about the gravity vectors is why is ##-mg## in the ##y-##axis equal to ##-mg\cos\theta## and the ##x-##axis is equal to...

In a certain anisotropic conductive material, the relationship between the current density ##\vec j## and the electric field ##\vec E## is given by: ##\vec j = \sigma_0\vec E + \sigma_1\vec n(\vec n\cdot\vec E)## where ##\vec n## is a constant unit vector. i) Calculate the angle between the...

1. Using the formula for the arc length; s= θr I have endeavoured to find the angle AOB sine both the arc length and radius are known; 11= θ*8 θ=11/8=1.375 rad I actually do not think that this can be correct as it seem to simplistic a response. Have I misinterpreted the question or used the...

These days, most particle physics anomalies (meaning, observations suggesting beyond-standard-model physics) eventually disappear under closer scrutiny. This one caught my eye because it can be attributed to the neutrino sector, which we understand least and which therefore has the most room for...

Attempt at solution in attachment.

I am working on developing a micro reflex sight and finally got the optical science of it sorted out, but now I reached a new impasse (hopefully the last really difficult one!). The device has to have an adjustment mechanism so the user can align the reticle with the bullet impact point, which...

Let ##μ_k## = 0.5 ##F_a## = 10 Newtons ##\theta## is the angel of the Applied force. How will the acceleration of the block change if the angle of the applied force is increase by ##5^o##? Write Increase, Decrease or Stay the same. Recently we were discussing a question similar to this in...

I tried solving this, the equation coming up is given by: θ≈4 cot^(-1)(e^(-3.1305 sqrt(1/R) t)). However, this is not correct as can be seen when plotted: enter image description here Can somebody please let me know, why is this equation not valid.?

I made a derivation of a general transform of the lorentz factor but i still looking in books that the lorentz factor is 1/sqrt(1-v^^2/c^^2) and my derivation is perfectly correct, my result is 1/(sqrt(1-v^^2*sin(a)/c^^2)+v*cos(a)), if we put here 90 degrees we get the classical lorentz factor...

So the statement says that in r(0)=0, so it departs from the origin. And it also says that v_y0 = 0, thus meaning thar it´´´ s position in the y direction is Constant. Is shooting in a π / 4 angle still plausible? or there´ s no way that can happen? So far I´ ve thought since there´ s no...

I know that on an alternating current circuit, you have to have both a line 1 and a line 2 to have a circuit. Here is a pictorial diagram of an alternating current circuit: In a previous thread, I asked why would an AC circuit like in Diagram 2 not work? Here is a photograph of diagram 2...

Hi PF! I keep seeing Kistler's contact angle model wrote like this $$ \theta_d = f(Ca+f^{-1}(\theta_e)) : f = \arccos\left( 1-2\tanh\left( 5.15 \left( \frac{x}{1+1.31x^{0.99}} \right)^{0.706} \right) \right) $$, where the plot then has a sort of break, something like this: But this is not the...

Here is my set up. Let t = theta for short tan(t) = 324/550 arctan(tan t) = arctan(324/550) t = arctan(324/550) Correct thus far? Note: What does "not to scale" mean in other words?

A 16 foot ladder is leaning against a house. It touches the bottom of a window that is 12, feet 6 inches above the ground. What is the measure of the angle that the ladder forms with the ground? I will use sin (x), where x is the measure of the angle that the ladder forms with the ground. I...

The beam of protons are directed towards the axis of the cylinder, perpendicular to the direction of the field. While traveling through the cross-section of the cylinder, the proton beam experiences a magnetic force, which tends to move the beam in a circular orbit of the radius given by: r =...

Preface to thread: I am darn well aware of the fact that on an AC circuit, there has to be a line 2 after the load to bring current back to the power source. This thread is about WHY does there have to be a line 2 after the load to bring current back to the power source. I hope that I don't...

I tried $$\Omega = \pi(\frac{\theta}{2})^{\frac{1}{2}}$$

My textbook says ##\vec r (\theta) = r \hat r (\theta)##, where ##\hat r (\theta)## is the terminal arm (a position vector in some sense). It can be seen that both ##\vec r (\theta)## and ##\hat r (\theta) ## are function of ##\theta##; whereas, the length of the vector ##r## is not. I...

Some time ago there was a problem with the following picture somewhere out here. I think this problem was underestimated a little bit. Let us reformulate the problem. Assume that each cylinder, if it was not influenced by the other one, could rotate freely about its fixed axis. But the...

I came across this diagram, the ##\gamma##'s are supposedly forces per unit length of the respective interfaces: It's not clear what these forces are acting on. ##\gamma_{SL}## and ##\gamma_{LG}## look like they could be acting on a small bit of water right at the end, but I have no idea what...

A single pair of points will be in contact between P and Q. The frictional force will try to make the velocity of these points equal. Say the final angular velocity of Q is ωq. The velocity of points in contact can never be equal because of difference in directions of ωq and ωp. If I break...

Hello, I have attempted the question below. I think i have correctly completed the question. Could anyone see if i have gone wrong? As trying to learn this. I am just worried about the units m to mm. Also the answer being correct, 917.6Gpa. I was unsure what units to use on the answer...

This is a rough sketch of the model. It is frictionless. I originally tried simple right-angle trig (sin θ =opp/hyp), but that just ends up as sin θ = sin θ , as well as cos θ = cos θ. I feel like there's also a way to manipulate dynamic equations around to equate something that is capable...

If it we know 3 sides of a right angle triangle, will it be possible to calculate the angles without using trig. Functions

Can anyone help me with a formula that would show the effect the counterforce of the neck will have on the direction the knife is moving, to be able to determine what a cut in a given direction what will be its direction of force? (I apologize for not following the guidelines for homework...

Given the total angles in the x direction, I set up this: (mg/cos(x))*sin(x)-Fe=0 then isolated for x: mgtan(x)=(kq^2)/(2*sin^2x) sin^2(x)*tan(x)=(kq^2)/(2mg) From here I am stuck. How do I go forward when x is contained in two different trig functions on the left?

I know that $\arccos{(\cos{\phi_1}\cos{\phi_2}+\sin{\phi_1}\sin{\phi_2}\cos{(\theta_2-\theta_1)})}=\gamma$ But how can i answer the above question? If any member knows the proof of this formula may reply to this question with correct proof.

Dear everyone, An airplane flies 470 miles from point $A$ to point $B$ with a bearing of 25 degrees. It then flies from 250 miles from point $B$ to point $C$ with a bearing of 40 degrees. Find the distance and the bearing from A to point C. Work I understand that I need to use law of...

Hi, Would it be correct to say that at Brewster's angle, all the incident light which has its electric field parallel to the plane of incidence gets refracted, and the rest of light whose electric field is perpendicular to the plane of incidence gets reflected? For example, if the light whose...

First, I attempted to find the wavelength of the incident wave in the required terms: Next, I tried to find the wavelength inside of the material: And then lasted, I tried to find the critical angle: My issue is that 1) I don't know if what I did was correct. 2) I don't think what I did...

Lets say that a man with a standing height of 185cm bent his knee 30 degrees, how many centimeters will be reduced from his standing height? Assume his femur length is 60cm and his tibia (shin) length is 50cm. Can anyone give me a hint? I've tried to use trigonometry but i don't think i fully...

Hey! :o We have a rectangle inside a semicircle with radius $1$ : From the midpoint of the one side we draw a line to the opposite vertices and one line to the opposite edge. Are the acute angles of the right triangles all equal to $45^{\circ}$ ? (Wondering) All four triangles are...

Balance the forces east-west: 3.5kg*sin45º + 4.2kg*cos30º - 4.8kg*sin30º - E*cosΘ = 0 E*cosΘ = 3.712 kg balance north-south: 2.8kg + 3.5kg*cos45º - 4.2kg*sin30º - 4.8kg*cos30º + E*sinΘ = 0 E*sinΘ = 0.982 EsinΘ / EcosΘ = 0.982 / 3.712 tanΘ = 0.2645 Θ = 14.8º ◄ E = 3.712kg / cos14.8º = 3.84...

I'm trying to make some simple rails for a makeshift server rack. I already have some aluminum angle (6063-T52) that has 2" legs and .125" thick. I have been trying to figure out how much weight could be safely held and can't find anything that makes sense. The weight load is fairly evenly...

ok, setting the force issues aside (for now), Id like to use what I know about triangles to figure how to position my linear actuator in order to open and close this door correctly: The vertical side is 84cm, the door is 92cm. The measured stroke of the AL is 25cm. I would need to lower the...

The problem of my question is the b part below: I know that the potential energy is just the gravitational potential energy, which is mgh(𝜃) = mg[(R+b/2)cos𝜃 +R𝜃sin𝜃], derived from the geometry. The equilibrium point is at 𝜃=0 and the system is a stable equilibrium for R>b/2. However, I have no...

Denote ##v=(1,2,3)^T##, ##\theta=\arctan(2)##, and ##\phi=\arctan(\frac{3}{\sqrt{5}})##.The way that I attempted this was by performing the following steps: (1) Rotate ##v## about the z-axis ##-\theta## degrees, while keeping the z-coordinate constant. (2) Rotate ##v## about the y-axis...

I've got the answer for (a). It's k = 0.78 N/m. I'm having problems with (b). I know that the equation of displacement in this case should either be : x(t) = Asin(ωt + φ) or x(t) = Acos(ωt - φ) where A = amplitudeFrom what I understand, both the equation above should give the same result as...

I have been trying to understand angle potentials such as described in this website, https://lammps.sandia.gov/doc/angle_style.html . Supposing two bonds have a certain angle they have to adhere to, what does this mean for that one atom being bound to, that only x amount of atoms can bind with...

Summary:: We have a rotating arm, offset from the centre of rotation by a certain length, which is controlled by varying the length of a control rod. Need the angle of the rotating arm in terms of length of the rod. The blue line is a fixed column structure. CE and BD form the rotational...

Given Theta1(angle of incidence) and alpha1(azimuth angle). how do we obtain the second reflection angle theta3 and alpha3? Assuming the surface to be a mirror reflection(theta1 = theta2). Need an equation when varied the incident angles we would obtain the second reflection angles or a method...

I first found the height of the ball after it's passed the 45 degree angle by doing 4.12*sin(45) = 2.9133, and plugged in the rest of the variables (masses cancel) .5(m)(vo^2) = (.5)(m)(vf^2) + mgh (17.5^2)(.5) = (.5)(vf^2)(9.8*2.9133) vf = 15.7845, however this is incorrect I don't understand...

I am a using a mirror to reflect an image at an angle of incidence of 10 degrees. The mirror is also at an angle of incidence of approximately 30 degrees from the viewer and it creates undesired reflections when looking at the mirror. Here is a diagram illustrating the situation. I am looking...

Hi, I am new here to the forum and I am having trouble with a project that I am undertaking with some friends. We are trying to build a firefighting robot. I am trying to derive an expression to solve for the launch angle theta of the water so that at x (meters), the projectile will be at 0.33...

From Ball 1 I can can determine it's initial velocity and then maximum height. I'm not sure how this is relevant, as I cannot find a formula using angle, time, height and velocity. I have found h=V(squared) x sin (squared) Theta / 2g and also t=2Vsin Theta/g. These give similar, but different...

I'm reading about x-ray diffraction in the context of crystal structure determination. Usually this discussion begins with Bragg's law, $$2d\sin\theta=n\lambda,$$ where ##\theta## is the angle of incoming and "reflected" x-rays. This is the bit that bothers me. I understand that the...

I decided to try and find a solution in a green (tilted) coordinate system. I started solving this problem with thinking about 1-rebound: ##⟹y=0, α=\text{angle under which we kick a ball}##; ##y=sin\alpha v_0t-\frac{1}{2}gt^2##; because I'm trying to solve this in a tilted system, I have to...