All Questions
37
questions
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33
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Rearranging trigonometric equation for low speed vehicle turning geometry
I have a set of equations that describe the geometry of a vehicle in low speed turning (a single track vehicle with the assumption that the tyres go in the direction they are pointing). A constraint ...
2
votes
0
answers
53
views
Optical path of a light ray reflected from two mirrors and into a pinhole camera
I have been staring at this problem for longer than I would like to admit.
I am trying to determine the path of a light ray from an object that is reflected from two plane mirrors and into the ...
- 21
5
votes
1
answer
796
views
Generalizing Lami's theorem
In statics, Lami's theorem is an equation relating the magnitudes of three coplanar, concurrent and non-collinear vectors, which keeps an object in static equilibrium, with the angles directly ...
- 1,011
0
votes
0
answers
88
views
Calculating a building's shade with building height
I work in GIS and to create a shade layer of a building, I need to "translate" the geometry/building or permanenently move it.
But I just need some help with my formula based on this video.
...
- 101
0
votes
1
answer
182
views
Expressing $\phi$ and $\theta$ in terms of time difference of arrival
I have an experimental setup consisting of three receivers with known locations $\langle x_i, y_i, z_i \rangle$, and a transmitter with unknown location $\langle x,y,z \rangle$ emitting a signal at ...
- 1,381
1
vote
1
answer
314
views
Maximum horizontal force that does not cause block to slide up ramp
You are sliding a block with mass m up a ramp inclined at an angle of $\theta$ with respect to the horizontal where the coefficient of static friction between the block and the ramp is $\mu_s$. What ...
- 1,225
6
votes
2
answers
190
views
When do two triangles reflected over midpoints have the same area?
Suppose I have a triangle ABC. I have points C', A', and B' on segments AB, BC, and CA, respectively. Suppose I reflect C' about the midpoint of AB to get point C'' (also on AB); similarly for the ...
1
vote
1
answer
69
views
Calculating angle from sphere
I'm trying to calculate the angle Phi in the picture in the case where the droplet is the perfect sphere I have the correct formula but I'm not sure how they found it. and I want to know the formula ...
- 29
0
votes
2
answers
432
views
How to generate random velocity vectors that can only move an object forward within a valid arc?
I have an object with known coordinates in in 3D but on the ground (z=0). The object has a direction vector. My goal is to move this object on the ground (so ...
- 435
5
votes
2
answers
491
views
Angle of mass hanging from two points connected at two points
I'm trying to calculate the angle (to the floor) a mass would hang if it were connected from either end to two points above it on the ceiling.
Let's call the distance between the points on the ceiling ...
1
vote
1
answer
237
views
Is there a way to find the intersection of two rectangles given their current velocity and position in constant time?
Suppose I have two rectangles, let's define them as $R_1$ and $R_2$, which each contain a length and width. Given the headings $\theta_1$ and $\theta_2$ respectively, as well as the coordinates $x_1, ...
- 11
0
votes
1
answer
58
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What is the meaning of this formula (y2-y1) * cos ((x1+x2) /2)? [closed]
Can anyone please explain the meaning of the cos((y1+y2)/2) in this formula please?
Note: the constant 6371 is the earth's radius
- 101
2
votes
1
answer
73
views
How to find the side of the triangle?
I need to find the value on the $v_{1}$ side of the triangle, the book's answer is $v_{1} = V cos(\psi) + v'_{1} cos (\theta - \psi)$, but I couldn't understand how you get to that result. I used the ...
- 81
19
votes
4
answers
608
views
A simple geometric problem, solving $f'(x)=\frac{f(x)}{\sqrt{r(x)^2-f(x)^2}}$, given $r(x)$.
Introduction
Suppose we have a convex, real function $f(x)$. We can define a tangent line to this function $t(x,s)$. Then, we can find the intersection of $t(x,s)$ with the $x$ axis. Let's call this ...
2
votes
1
answer
57
views
Two rays/vectors that satisfy $\Delta \mathbf{k} = \mathbf{k} - \mathbf{k}_0$ make the same angle with perpendicular plane?
This question is from physics, but I think the answer is more-so fundamentally a fact of mathematics, rather than physics which is why I'm posting it here.
My textbook, Solid-State Physics, Fluidics, ...
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