Time dilation & length contraction

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Homework Help Overview

The discussion revolves around problems related to time dilation and length contraction in the context of special relativity. The original poster presents a scenario involving an astronaut traveling at relativistic speeds across the galaxy, seeking assistance with calculations related to perceived time and length during the journey.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the application of relevant equations for time dilation and length contraction. Some express difficulty in starting the calculations and seek initial guidance. Others share their progress on specific problems, indicating a mix of understanding and confusion regarding the mathematical steps involved.

Discussion Status

There is active engagement, with some participants successfully solving parts of the problem while others are still grappling with the initial steps. A participant acknowledges a mistake in their calculations, suggesting that the discussion is moving towards clarification and correction of misunderstandings.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the amount of direct assistance they can receive. There is an emphasis on understanding the concepts rather than simply arriving at the correct answers.

riddledum
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Hi guys and girls. Need some assistance with these problems, not the hardest examples, but I need some help on the way.


Homework Statement



1.

An astronaut travels at 0.9c across our galaxy, which is 100 000 light years in diameter. How long time will it take (according to the astronaut) to travel from one end of the galaxy to the other?

2.

Same question, but in this question, the astronaut travels at 0.99c

3.

If the astronaut travels at 0.99c, he will perceive the length of the galaxy to another length, what is that length?




Homework Equations



L' = L*sqrt(1-v^2/c^2)

t' = t/sqrt(1-v^2/c^2)
 
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What have you tried?

Where are you stuck?
 
As always, I have trouble getting started and getting my head around what to do and how. Some small tips to get started would be appreciated.
 
Managed to solve both 2 and 3 now
 
1. is just about like 2.
 
What am I doing wrong here?


t' = t*sqrt(1-v^2/c^2)

t' = 100000*sqrt(1-0.9c^2/c^2)

t' = 31622.7766
 
Where did you get t=100000 from? You also messed up crunching the numbers. Line 3 doesn't follow from line 2.
 
Woops, saw what I did wrong there & Got the right answer immediately. Thanks a lot!
 

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