Why Can't I Use Time Dilation to Calculate Relative Time for the Ball?

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SUMMARY

The discussion centers on the inability to use time dilation to calculate the relative time for a ball's travel in relativistic contexts. Participants emphasize the importance of employing relativistic velocity-addition formulas and gamma factors for accurate calculations. The conversation highlights that while time dilation is a critical concept in relativity, it cannot be directly applied to all scenarios involving relative motion, particularly when velocity transformations yield different results. This underscores the necessity of understanding the nuances of relativistic physics.

PREREQUISITES
  • Understanding of special relativity concepts, including time dilation and velocity addition.
  • Familiarity with gamma factors and their calculations in relativistic contexts.
  • Basic knowledge of physics problem-solving techniques related to motion.
  • Experience with mathematical manipulation of relativistic equations.
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  • Study the derivation and application of the relativistic velocity-addition formula.
  • Learn how to calculate gamma factors for various velocities in special relativity.
  • Explore examples of time dilation and its limitations in different scenarios.
  • Investigate the implications of velocity transformations on time measurements in relativity.
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Students of physics, educators teaching special relativity, and anyone interested in understanding the complexities of time and motion in relativistic frameworks.

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I agree with a, b, and c1.

I'm not sure about c2, it might be correct. I would have used the relativistic velocity-addition formulas.

When I used to work out these kinds of problems, I would write down values of any gamma factors I calculate along the way. That saves time, not having to recalculate it when they often get used repeatedly. It's also an intermediate check, when I'd end up with a wrong answer and am tracking down where the mistake was.
 
Yea. Velocity transformation is another way of doing it. But the answer is different. Why I can't use time dilation to calculate the relative time taken for the ball to travel in this case?
 

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