Geometry: I want to understand some points

  • Thread starter Thread starter irony of truth
  • Start date Start date
  • Tags Tags
    Geometry Points
AI Thread Summary
To find the unknown x related to an arc of a great circle 10 units long receding from its chord, the relationship between the radius R and angle alpha is crucial. The discussion suggests that x can be expressed as R - R cos(alpha), representing the maximum distance between the arc and the chord. The geometry involves an isosceles triangle formed by the endpoints of the arc and the center of the circle. Additionally, properties of triangles indicate that the angle can be determined to be 45 degrees, leading to R being calculated as the square root of 50. Understanding these relationships is essential for solving the problem effectively.
irony of truth
Messages
89
Reaction score
0
What is my unknown (say x) if I am finding the value in which an arc of a great circle 10 units long recedes from its chord? (given radius R and angle alpha?)

Here's my figure as an attachment...
 

Attachments

  • s the figure.JPG
    s the figure.JPG
    5.8 KB · Views: 521
Physics news on Phys.org
I am guessing, you can express R = xR + (1-x)R where (1-x)R is the height of your (isosceles) triangle and xR is the bit from the chord to the circle.
 
Last edited:
What do you mean by "recedes from its chord"?
 
HallsofIvy, seems like the arc is moving away from its respected chord (form by the two enddpoints of the arc)

My friend told me that x = R - R cos (alpha)... I wonder why...
 
He has given the greatest distance between the arc and the chord i.e. the difference of the radius and distance of the chord from the center
 
hi
By using the laws properties of triangle you will get the angle to be 45 degrees and
R to be square root of 50

http://www.mathsrevision.net/gcse/pages.php?page=47
 
Last edited by a moderator:

Thread 'Rolling without slipping on a curved surface'

Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
View full post »
Thread 'Trying to understand the logic behind adding vectors with an angle between them'

Thread 'Trying to understand the logic behind adding vectors with an angle between them'

My initial calculation was to subtract V1 from V2 to show that from the perspective of the second aircraft the first one is -300km/h. So i checked with ChatGPT and it said I cant just subtract them because I have an angle between them. So I dont understand the reasoning of it. Like why should a velocity be dependent on an angle? I was thinking about how it would look like if the planes where parallel to each other, and then how it look like if one is turning away and I dont see it. Since...
View full post »
Thread 'Correct statement about a reservoir with an outlet pipe'

Thread 'Correct statement about a reservoir with an outlet pipe'

The answer to this question is statements (ii) and (iv) are correct. (i) This is FALSE because the speed of water in the tap is greater than speed at the water surface (ii) I don't even understand this statement. What does the "seal" part have to do with water flowing out? Won't the water still flow out through the tap until the tank is empty whether the reservoir is sealed or not? (iii) In my opinion, this statement would be correct. Increasing the gravitational potential energy of the...
View full post »

Similar threads

The speed of the point of intersection of two uniformly moving lines
Replies
24
Views
2K
Electric Field from a Charged Semicircular Rod
Replies
2
Views
3K
Angle of deviation from a magnetic field
Replies
5
Views
2K
Solving Semi-circle Inside Triangle Geometry Problem
Replies
13
Views
3K
Electrostatic potential due to a dipole
Replies
7
Views
3K
In which direction is the magnetic field at point P?
Replies
12
Views
2K
A moving boat with a flag on its mast
Replies
15
Views
1K
Frequency & Wavelength of a Vibrating Wire
Replies
5
Views
1K
Aeroplane follows circular trajectory-Tension? (geometry)
Replies
6
Views
2K
The components of force and velocity vectors in circular motion
Replies
11
Views
3K

Hot Threads

Recent Insights

Back
Top