this post was submitted on 28 Aug 2024
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They're traveling away from their origin at constant velocities, so they're traveling relative to each other at constant velocities as well.
The magnitude of the resulting vector (i.e., speed) can be calculated trivially since their movement is perpendicular on a plane, as the root of sum of squares, which many could recognize as the Pythagorean theorem:
√((5 ft/s)² + (1 ft/s)²) = √26 ft/s ≈ 5.1 ft/s
You can verify this by finding that their average speed apart is the same at all times (for all t > 0):
Vavg = √((t * 5 ft/s)² + (t * 1 ft/s)²) / t = √(t² * ((5 ft/s)² + (1 ft/s)²)) / t = √26 ft/s
https://en.m.wikipedia.org/wiki/Spherical_geometry
I couldn't find 'potatoy geometry' for a better approximation of earth.
You'll note that I already assumed that they were on a plane, not the surface of a sphere.
I'm also noting the stick up your ass. 🙄
If the potato remark and subreddit don't tip you off that I was being flippant, I don't know what will.
No, the stick would be a one-dimensional line.