Calculating Light Signal Velocity: Relativistic Effects at 0.5c

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SUMMARY

The discussion focuses on calculating the velocity components of a light signal fired at 60° north of west, as observed by two different observers moving at 0.5c. The relevant equations used are the relativistic velocity addition formulas: U' = (u-v)/(1-uv/c) and U = (u+v)/(1+uv/c). The challenge lies in incorporating the angle into the calculations, specifically using trigonometric functions to determine the components of the light signal's velocity. The participants emphasize the importance of correctly applying these formulas to achieve accurate results.

PREREQUISITES
  • Understanding of special relativity and relativistic velocity addition
  • Familiarity with trigonometric functions, particularly sine and cosine
  • Knowledge of vector components in two-dimensional motion
  • Basic understanding of light signal properties and speed of light (c)
NEXT STEPS
  • Study the derivation and application of the relativistic velocity addition formulas
  • Learn how to resolve vectors into components using trigonometric identities
  • Explore examples of relativistic effects at various speeds, particularly at 0.5c
  • Investigate the implications of relativistic effects on time and space perception
USEFUL FOR

Students and educators in physics, particularly those studying special relativity, as well as anyone interested in understanding the behavior of light signals in relativistic contexts.

Engineergirl2
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Homework Statement



You fire a light signal at 60° north of west. (a) find the velocity components of this signal according to an observer moving eastward relative to you at 0.5c. From them, determine the magnitude and direction of light signal's velocity according to the other observer. (b) find the components according to a different observer, moving westward relative to you at 0.5c.

Homework Equations



U'= (u-v)/(1-uv/c)
U= (u+v)/(1+uv/c)

The Attempt at a Solution



These are the only two formulas that I could think to use, but I am not sure how to incorporate the angle? It's throwing me off of the whole problem. Any help or explanation would be so much appreciated, thank youu!
 
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Would I use the speed of light for the hypotenuse of my triangle, since it says I'm firing a light signal, and then use simple trig, i.e. Csin60=y for my y-component? I'm really unsure.
 

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