Question on movement speeds relative to an observer.

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Discussion Overview

The discussion revolves around the relative movement speeds of two individuals, Gary and Liam, as observed from a fixed point. The scenario involves circular motion and the conditions under which Liam can appear to move at the same speed as Gary while maintaining a specific distance from the observer. The conversation explores both the mathematical and conceptual aspects of relative motion.

Discussion Character

  • Exploratory
  • Mathematical reasoning
  • Conceptual clarification

Main Points Raised

  • One participant suggests that Liam must travel at 10 metres per second to match Gary's apparent speed, while another initially states it is 5 metres per second.
  • A later post clarifies that Liam needs to start moving slightly before Gary to remain hidden behind him, indicating a need for timing in addition to speed.
  • Another participant elaborates on the calculations involved, detailing the circumferences of the circles each person travels and deriving Liam's required speed based on the time it takes for Gary to complete his circular path.
  • There is a discussion about the geometrical subtended area and the implications of light delay in the context of their sizes and distances, introducing potential complexities related to relativistic principles.

Areas of Agreement / Disagreement

Participants express differing views on the required speed for Liam, with some asserting it is 10 metres per second and others suggesting it could be 5 metres per second. The discussion remains unresolved regarding the exact conditions and calculations needed to determine Liam's speed.

Contextual Notes

The discussion includes assumptions about the sizes of Gary and Liam, as well as the effects of light delay and relativistic principles, which are not fully resolved and may affect the conclusions drawn.

Ralphonsicus
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Say I am at point X. My friend, Gary, is 20m from X, and my friend Liam is 40m from X. Gary is traveling at 5 metres per second in a circle around me, remaining 20m from X. What speed must Liam travel at to appear, to me, to be traveling at the same speed as Gary? Is it 10 metres per second or is it more complicated?
 
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5 metres per second.
 
ghwellsjr said:
5 metres per second.

Maybe I phrased it wrong. Imagine that Liam wants to stay hidden behind Gary as Gary walks, while Liam himself remains 40m away, and Gary 20m?
 
10 metres per second. But Liam will have to start walking a little before Gary in order to stay hidden.
 
It's 10m/s, Liam is going to have to run as fast as Usain Bolt.

Gary's circle of radius 20m has a circumference of pi*D, where D is diameter = 2*20m
So, Gary's circle is about 125.6m around. If he walks 5m of that in one second, then the time around is 125.6m/(5m/1s)=125.6ms/5m=25.12s
Liam would need to walk his circle in the same time as 25.12s
The circumference of Liam's circle is pi*D where D is 2*40m, or 251.2m
Liam needs to go 251.2m in 25.12s, so 251.2m/25.12s=10m/s

George, unless Gary is very thin and Liam pretty fat (for a thought experiment both might be considered identical sized spheres), Liam should subtend a small enough area behind Gary that his image will stay well within that subtended by Gary with plenty of overlap to account for the delaying of his light image, at least at these distances.
But I guess the next step you are anticipating would be to determine the sizes of Gary and Liam, and the respective distances at which the geometrical subtended overlap is overcome by the delay in light. That calculation would be complex because the segment of arc subtended by Gary or Liam would intersect them (if they were spheres with their centers located on the circumference of their walking circles) not as a diameter of their sphere, but as less than their diameters (a little closer to the central observer)... and by then there might be numerous relativistic principles to consider.
 
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