Tagged Questions
0
votes
1answer
52 views
Calculating the angular velocity
I have an inverted pendulum with a accelerometer mounted on the top that at rest gives me a vector up opposite to gravity, which is used to calculate the angle of the pendulum. Is it possible to ...
3
votes
1answer
138 views
How is the formula for the focal point of a ball lens derived?
In Optical Design Fundamentals for Infrared Systems 2nd ed., Mr. Riedl writes:
A sphere or ball performs surprisingly well as a lens. At closer
scrutiny, one fmds that such an element can be ...
1
vote
2answers
28 views
Trigonometry in the DE
Just a simple undergrad physics student asking them mathematicians.
I have a very simple 2nd order homogeneous DE of the form:
$$y''=-a^2y$$
So, a solution will be of the form $$y(t)=c_1 ...
1
vote
1answer
101 views
Phi vs Theta referring to angles of vectors
Even though this question arises from doing simple vector math from a physics textbook I figured it's much more general than that application.
The problem is as follows:
A spelunker is surveying a ...
1
vote
1answer
71 views
How to calculate the position of a turning object, based on its rotation?
I'm working on a program that periodically updates the position of an object. The object is able to move in straight lines, as well as turn gradually. In order to check that my object is turning ...
4
votes
0answers
109 views
Integral of a gaussian function of trigonometric functions
I need help with the analytical solution of this integral:
...
1
vote
0answers
42 views
Simple equation misunderstanding
Im trying to use an equation on this page
http://en.wikipedia.org/wiki/Bicycle_and_motorcycle_dynamics
The angle of lean, $\theta$, can easily be calculated using the laws of circular motion
$$ ...
0
votes
0answers
121 views
sinusoidal word problem
in tidal waves the sea level drops first leaving the seabed exposed (normally 30 feet below sea level), then it rises a equal distance above sea level. waves hitting a city have a max height of 38.9 ...
2
votes
1answer
113 views
How to simultaneously solving trig equations?
I was doing some math work, and have to solve two trig equations simultaneously, but have no idea how to approach this, can anyone help, just need to be pointed in the right direction.
I have to ...
1
vote
1answer
66 views
How $v=(-\sin\frac{\alpha}{2}\sin\frac{\beta}{2},\cos\frac{\alpha}{2}\sin\frac{\beta}{2},\sin\frac{\alpha}{2}\cos\frac{\beta}{2})$ is derived from…
In the book Quarternion and Rotation Sequences, I can't seem to work out how the final equation (colored in $\color{red}{red}$) is derived from the original equation (colored in $\color{blue}{blue}$).
...
7
votes
1answer
336 views
Does apparent retrograde motion of planets begin and end at quadrature?
I've read it several places that the apparent retrograde motion of planets (during which they seem, as viewed from Earth, to move in the opposite sense of their normal "direct" orbital motion against ...
-1
votes
1answer
98 views
Function whose graph resembles the shape in this image
What is the function whose graph would resemble the shape found in the image below?
I looked this up on Wikipedia, tried making my own, but I can't find an equation the Electromagnetic Spectrum. I ...
1
vote
3answers
203 views
Projectile Motion
Hello Stack Exchangers!
I'm developing a video game. One feature requires an archer be able to target an enemy and shoot an arrow at it. I've looked around and found plenty of guides on how to do ...
0
votes
1answer
116 views
Acceleration along a 2D plane
It's been a long time since I've done trig, and I never new it very well. I have a problem I don't know how to solve.
I have an object on a 2D plane that I want to move. I have this objects x and y ...
1
vote
2answers
304 views
Homework help with projectile motion
I would please like help on the following question related to projectile motion.
A horizontal drainpipe 6 metres above sea level empties stormwater into the sea. If the water comes out ...
0
votes
1answer
161 views
Simple harmonic motion and trigonometry
Here's the question I would like help with:
A particle is moving in simple harmonic motion according to $x=6\sin
\left (2t+\frac{\pi }{2} \right )$. Find the first two times when the
velocity ...
1
vote
1answer
122 views
Simple Harmonic Motion with trigonometry
I need some help with my high school maths question:
A particle is moving in simple harmonic motion has speed 12m/s at the origin. Find the displacement-time equation if it is known that for positive ...
2
votes
2answers
111 views
Trigonometry in Simple Harmonic Motion
In one of my high school maths questions the example given to find the maximum displacement of a Simple Harmonic Motion where
$ x=2+4\cos \left (2t + \frac{\pi}{3} \right ) $
and the motion lies in ...
1
vote
1answer
49 views
The Law of Sines and a second forces magnitude
How do you solve for the second forces magnitude? The 17' and 30' threw me off.
0
votes
2answers
417 views
Velocity, Radius and Angular Speed - Finding Units
I have been trying to figure this one out for two days, and I really have no idea what to do.
To begin with, I need to know what units will be produced in the following situations:
Velocity's ...
3
votes
1answer
605 views
Finding force for trajectory
Using the trajectory equations provided on hyperphysics, I have developed some code to plot the trajectory of an object. I now need to work out the x and y forces to apply to make the object follow ...
0
votes
1answer
152 views
Solution for following trigonometric equation?
I have the following trigonometric equation in $\theta$:
$$0=G_{\omega}(1/r^2)({\csc^2}\theta){(r\cos\theta-x)}^2+(\cot\theta)(r\cos\theta-x)+r\sin\theta-y.$$
Is there an analytical solution for ...
2
votes
1answer
106 views
Finding Angle of Elevation to hit X, Y
My ultimate goal is to find the angle of elevation necessary to launch a projectile from the origin to (x,y) with initial velocity V and under gravitational acceleration g. Wind resistance is ignored.
...
1
vote
1answer
56 views
find point of object in the future given direction and velocity
I have a point A, and another point B. I know the distance from point A to B. I also know the velocity with which B is moving and its direction. I also know the angle of B with respect to A. I would ...
0
votes
2answers
101 views
Touch up on Trig
I have forgotten a few things about trigonometry and angles.
I have this trig equation, $\sin \theta = \frac{200\text{ dyn}}{224\text{ dyn}}$
What exactly are the steps of getting the angle, ...
3
votes
2answers
323 views
Diffraction and Computer Generated Holography Calculations
I've tried this through Mathematica, and hit my own limit in math ability trying to do this, both to no avail. I'm assuming there is no way to do so, as a simple solution to this problem would be a ...
3
votes
1answer
439 views
How to find angle of motion in frictionless space based on vx and vy
This might, perhaps, be more suited to Stack Overflow or the Gaming section, but since it's math that is above my head, I thought I'd come straight here for it.
I'm making a space game. So far I ...
2
votes
1answer
433 views
What does the little d and d^2 mean in equations?
I'm reading a text on ray tracing. There is this section about radiometric quantities where radiance is defined as
$L = \frac{d^2\Phi}{dA cos\Theta d\omega}$
$\Phi$ is the radiant flux
$\Theta$ is ...
0
votes
1answer
302 views
Is it possible to calculate an angle of movement from the horizontal from accelerometer and magnetometer data?
I have a home made device (think baseball) with an accelerometer and a magnetometer embedded within it and would like to capture some details of an attempted 'throw' of the device.
All I need is the ...
2
votes
2answers
416 views
What is the optimal angle when throwing a stone on a slope?
The question what-is-the-optimum-angle-of-projection-when-throwing-a-stone-off-a-cliff was asked and answered a while back. This one has a much cleaner answer. Now you are on a uniform slope, a line ...
7
votes
2answers
1k views
What is the optimum angle of projection when throwing a stone off a cliff?
You are standing on a cliff at a height h above the sea. You are capable of throwing a stone with velocity v at any angle a between horizontal and vertical. What is the value of a when the horizontal ...
