Is there a way to calculate this transformation?

  • #1
wirefree
103
21
Namaste & G'day!

Imagine a helicopter view of a Polo ground. It's length & breadth are known.

Screenshot_20240316-165049.png



Now you are seated where the blue dot is. Your view is such:

IMG_2024-03-16-16-48-17-200~2.jpg


How do mathematicians calculate the distance travelled by a ball from the second perspective?

From the top view, this would be trivial.

But now your view is transformed.
 
Mathematics news on Phys.org
  • #2
I think of the second prespective in cylindrical coordinates (r,θ). θ is “easy” to determine, r is more difficult. In a perfect world, one could measure the diameter of the ball to determine its distance. There are other experimental techniques, but I am unsure exactly what you are looking for.
 
  • Like
Likes FactChecker
  • #3
Suppose the eye-point location is at the center of the polar coordinates (##r_{eye}=0##) and the angle, ##\theta##, of the polar coordinates of the ball are known. The distance to the ball location, ##r##, remains to be determined. Assuming a flat earth, ##r## can be calculated using trigonometry. You would need to know the distance to the tree-line. That tree-line has sides and its distance would require some calculations that depend on the direction.
 

Similar threads

  • Special and General Relativity
Replies
29
Views
2K
  • Special and General Relativity
Replies
27
Views
1K
  • Precalculus Mathematics Homework Help
Replies
4
Views
1K
  • Special and General Relativity
Replies
25
Views
763
Replies
1
Views
2K
  • Classical Physics
Replies
21
Views
985
  • Introductory Physics Homework Help
Replies
6
Views
915
  • Special and General Relativity
Replies
5
Views
1K
  • Engineering and Comp Sci Homework Help
Replies
4
Views
1K
  • Special and General Relativity
Replies
27
Views
2K
Back
Top