Angle Definition and 1000 Threads

Homework Statement The refractive index of diamond is 2.42. A ray of light passing from the inside of a diamond into air makes an angle of incidence of 20 degrees. Find the angle of refraction. Homework Equations n = refractive index aNd = 2.42 (my book said the speed of light in a vacuum and...

Here is the problem: I am sure I can use pythagorean theorem of quadratic equation to solve but to be honest I'm blanking ridiculously. I have tried setting it on a coordinate grid and finding the resultant, but I have had no luck! I know I've done this problem before in high school but I'm...

I'm really lost on this one. I'm really not sure how to get started on this. I started it out as a force problem and solved for ax = g*cos(theta). I then integrated that (treating it like a constant) from zero to D to find my initial velocity at the time the block reaches the edge of the...

Homework Statement [/B] A baseball player hits a ball 200.0m home run. The ball travels at angle of 45° with the horizontal just after being hit. Determine the initial speed. Assume the ball lands the same height it was hit. 2. Homework Equations The Attempt at a Solution I am not sure how...

Homework Statement Given the diagram below, showing the path of a geocentric satellite S flying over a ground station G, find an expression for the geocentric semi-angle ##\phi## in terms of ##\epsilon##, the radius of the Earth ##R_E##, and the height of the orbit ##h##. Homework Equations...

Homework Statement Instructions for finding a buried treasure include the following: Go 65.0 paces at 249deg, turn to 134deg and walk 134 paces, then travel 101 paces at 168deg. The angles are measured counterclockwise from an axis pointing to the east, the +x direction. Determine the resultant...

Homework Statement A uniform bar with length c can slide a cylindrical surface with a radius of r. Determine the maximum angle theta that guarantees the equilibrium of the bar if the friction coefficient at the points of contact is u. Homework Equations Friction force = u*N (where N is the...

Homework Statement Find: The angle between the force vector and the line AO, and the magnitude of the projection of the force along the line AO Homework Equations cos(theta)=(A*B)/(|A|*|B|) The Attempt at a Solution I thought that since I'm given the force F in cartesian form, that I would...

Homework Statement Each one of the force vectors are surrounded with dimensions. But you're not given any angles. How do you solve for the resultant vector like that? Homework Equations Fr = F1 + F2 + F3 The Attempt at a Solution I tried taking the arctan(200/210) on the 435 N vector to...

My textbook (on celestial mechanics) makes a passing reference to position on an ellipse being expressed as: ##r = a(1 - e \cos E)## before moving on to the substance of the chapter. E is the eccentric anomaly, and r is the distance from the focus to the point on the ellipse. I'm trying to...

Dear everyone,Direction Write the vector in component form. v lies in the yz planeplane, has magnitude 2, and makes an angle of 30 degrees with the positive y axis. Work I know that the x component is zero. <0,v1,v2​> Thanks Cbarker1

Looks like this question is going to make a long thread. :) This is what the problem states Using the pair of compass and a straight edge, Then, After That, Thereafter, Thereafter, The question states to mark the point where the tangent and AD produced as 'X'.Now can you help me...

Please show me the relationship that proves how an inclined plane's angle of incline, θ, is equal to the angle used to find the components of gravity force. I know that the angles are the same, but I'd like a way to show it. Thanks!

Hi all Tearing my hair out trying to calculate the Maximum acceptance angle for a problem. Experiment involved shining a laser into a tube of water. I have calculated the angle of refraction based on the average of two critical angles (one known and one measured manually) as 52.49 degrees...

What is the angle of intersection between the two planes in ℝ3 with general equations x-y=5 and y-z=7? I know that the angle between then is equal to cos-1 (u⋅v/||u|| ||v||) but I am stuck on the general equations given, how can I solve when given these ?

If the the question is too small , Please be kind enough to read it from here Question The interior angles of a pentagon add up to 540 degrees. So thinking that this is a regular pentagon with all 5 sides equal an interior would be 108 degrees. And speaking of the square All four sides are...

Homework Statement Calculate the force on the cilinder. You need the angle of the tangent and r. Homework Equations Down under here. The solution for the angle is 30°. But why does the formula I used did not work out? My solution is 40,9°, why isn't this correct for this excercise? The...

Homework Statement Show that the equation of the chord joining the points P(a\cos(\phi), b\sin(\phi)) and Q(a\cos(\theta), b\sin(\theta)) on the ellipse b^2x^2+a^2y^2=a^2b^2 is bx cos\frac{1}{2}(\theta+\phi)+ay\sin\frac{1}{2}(\theta+\phi)=ab\cos\frac{1}{2}(\theta-\phi). Prove that , if the...

Homework Statement Find x[/B] Homework Equations a+b+c=180[/B]The Attempt at a Solution ADB= 65+65+50=180 How do I find x in DBC?

For example, the term angular frequency, it units is radian per second. For phase, it is also measured in radians or degrees, why is that? Why is the math the same when you use angles to describe oscillations?

Homework Statement Find what x is I don't understand what to do with (3x-23). Homework Equations Angles centered at a point: a+b+c+d=360 https://drtayeb.files.wordpress.com/2011/03/igcse-math-extended.pdf (here is a pdf of the textbook, Exercise 4A, 3i.)[/B]The Attempt at a Solution...

Say there are two lines that can be described as y=m1x + c1 and y= m2x + c2; they intercept at the point (x, y). There's a line that will bisect the angle that the two lines form as they intercept and it can be described as y= m3x + c3; this line will also intercept the other two lines at (x...

Why is the term ##(\sin\theta\,\dot{\theta})^2## fourth order in the small ##\theta##, as claimed by the sentence below (5.108)? By small-angle approximation, ##(\sin\theta\,\dot{\theta})^2\approx\theta^2\,\dot{\theta}^2##. For this to be fourth order, it seems like we must have...

Homework Statement I know that an element that is subjected to max shear stress is 45 degree away from position of an element that is subjected to principal stress.I couldn't understand why the θ s= θ p -45 degree? Cant it be θ s= θ p +45 degree ? Homework EquationsThe Attempt at a Solution...

Hi, As told in the problem I drew a figure, Next the magnitude of $$\angle BHL$$ should be found using trigonometric tables. Can you help me to and find the angle BHL (Smile) Many Thanks (Smile)

Find the value of angle X 'BC & CD pints are on BE side of triangle ABE. Find the Value of angle X' :)

Homework Statement this is actually mohr's circle formula, forget about the theory,let's focus on the mathematics part. I couldn't understand why the tan( 2 θs1) = -(σx -σy) / 2τxy ? 2θs1 is outside the triangle Homework EquationsThe Attempt at a Solution theorically, tan(180-α )= -tan( α ) ...

1. A uniform bar AB of length 3 m and weight 40 N rests in equilibrium with the lower end A on a smooth plane inclined at an angle alpha to the horizontal, where tan alpha = 3/4 and a point C of the rod against a smooth peg. If the rod makes an angle theta with the horizontal, where tan theta =...

Homework Statement A projectile is fired with a velocity of 60 m per second at an angle, theta, from a horizontal ground towards the roof of a tunnel of height 5m. If the projectile just barely touches the roof, determine the a) angle of projection b) time of the flight c) range of the...

Hello everyone, i'm new to the forum so hope it is the right place for my question :) i need to know the angle between two triangular surfaces, the easiest way would be extract the normal for each surface(u,v) and then using the dot product we can easily compute the cosine for the angle I'm...

There are lots of basic explanations on the Internet of the two most famous uncertainty principles, that of momentum-position and Energy-time, but I do not find any basic explanation of the action-angle uncertainty principle. I do not even know what angle (or what operator) is being referred to...

I am looking for sources which describe how to measure the contact angle between immiscible liquids in a tube. The literature seems to be extremely lacking so if anyone has any knowledge I would appreciate the help.

I'm having trouble finding any sources which describe how to accurately measure the contact angle between immiscible liquids in a tube. Any help would be appreciated.

I think this should be equal to the famous precession angle, but with a negative sign: ##d\phi = 6\pi m/r## correct?

I recently decided to take a whack at this problem. Came up with an interesting approach, thought it would make a good conversation topic. Anyone else tried to do this? What were your results?

Assume a flat one square foot vertical plate attached 6 feet up, outside on a wall. Dozens of yards away are various solar reflectors angled to reflect sunlight onto that plate. Problem is, the plate requires to be only struck straight on at a 0 degree angle of incidence. And, all the...

Hi all, I'm slowly working through "Mathematical Methods in the Physical Sciences" by Mary Boas, which I highly recommend, and I'm stumped on one of the questions. The problem is to prove the double angle formulas sin (2Θ)=2sinΘcosΘ and cos(2Θ)=cos2Θ-sin2Θ by using Euler's formula (raised to...

Homework Statement This problem asks for the angle on an inclined plane-- I have attached the problem below. Homework Equations fnet=ma The Attempt at a Solution I honestly have no idea what to do. I found the vector components for gravity and made a FBD for the box, but I can't really figure...

I have been on the hunt looking for a precise equation that gives you the angle that a ship is displaced along its x-axis (roll). There is a somewhat simple equation:Roll angle (Θ) : Θ = Acos( ωt+ φ)------where A is the amplitude of the wave, ω is the frequency and φ is the phase chage. So...

Homework Statement A light ray falls from the air (##n_a=1##) into the center of the upper surface of a long cilindrical glass tube with an index of refraction ##n_t=3/2##. The tube is submerged into water all the way to the upper edge and the waters index of refraction is ##n_w=4/3##. What is...

Hi everybody, I would like to know what would be the best angle (or best geometry) to put the detector relative to the light source in order to observe the emission radiation from the fluorescent materials? As I know the most common geometry used for fluorescence is right angle observation...

The forces acting on the glider are the gravitational force, the lift force and the drag (air friction). The drag () and lift force () are a function of the angle that the wings have with the gliding direction. =122 with: =0.1+3∙10−32 =122 with: =0.2+0.1− 3∙10−32 In the above equations, is in...

Homework Statement You have been stranded on a deserted island. Fortunately, you managed to bring a flare gun. You can see a ship 300. m off shore. Unfortunately, because of the daylight the ship cannot see your flare unless it is within 100. m of the ship. A.) If you fire the flare gun from...

Homework Statement You come to a river and you see a vine you will use to swing across. Your mass is 75.0 kg, the vine is 18.0 m long, and the vine breaks when under 655 N of tension. a) at what angle from the vertical will the vine break? b) what should be the maximum tension supported by the...

What is the equation for how a light beam is bent by a mass? Say a mass M way out in space, and a light beam is aimed from VERY far away such that it should pass at a radius R from the mass.

Homework Statement A projectile was launched from the top of a 100m tower upward at an angle theta to the horizontal with an initial velocity of 36m/s. The time of flight of the projectile was 8 seconds. Determine: i) The angle of projection ii) The maximum height reached by the projectile...

Homework Statement Homework EquationsThe Attempt at a Solution Here is what i have done so far: Fx = cos 45 T - Ff =ma Fy=sin 45 T -mg+ Fn =ma I found ff= uk * Fn = 0.5 *sin 45 +mg fn = sin 45 +mg Isolated for T in the x and y: Tx = ma + Ff / cos 45 = 13.404 Ty = ma +mg - Fn / sin 45 =...

Homework Statement Two vectors of magnitude 5 units and 3 units are added such that the angle between the resultant and the vector of magnitude 5units is maximum. Find this angle. Homework EquationsThe Attempt at a Solution Knowing that the resultant vector makes a smaller angle with a...

A body in an absolute vacuum is suspended from an axle having no friction at the body or at the suspension points. A power source is affixed to the body which rotates the axle. At rest the body is horizontal. The body weighs 4000 lbs. The center of gravity of the body is vertically 4 ft. below...

This is the problem I am looking to solve: given two objects of different mass, find the angle of deflection after an elastic collision for each object. For both objects we know: m : Mass in Kilograms θi : Initial Angle in Degrees si : Initial Speed in Units per Second sf : Final Speed in...