How Long Will It Take to Travel 65 Light-Years at Relativistic Speeds?

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Homework Help Overview

The problem involves calculating the time taken to travel to a star 65 light-years away while experiencing relativistic effects, specifically length contraction and time dilation. The original poster is attempting to reconcile the perceived distance of 25 light-years with the actual distance of 65 light-years.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the use of length contraction and time dilation equations to find the velocity and time taken for the journey. Questions arise about the necessity of time dilation when distance and velocity are known in the same frame. There is also confusion regarding the application of these concepts in the context of the problem.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the problem and questioning the application of relativistic equations. Some guidance has been offered regarding the relationship between distance, velocity, and time, but no consensus has been reached on the correct approach.

Contextual Notes

Participants note the challenge of combining length contraction and time dilation concepts, indicating a potential misunderstanding of the problem setup. There is also an acknowledgment of the confusion surrounding the use of light-years as a measure of distance in this context.

persephoneia
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Homework Statement


Suppose you decide to travel to a star 65 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip?

Homework Equations


∆t=∆t0/(√ (1−v2/c2 )) / ∆t0 = ∆t √(1−v2/c2)
L=L0√ (1−v2/c2)

The Attempt at a Solution


I've attempted to use the length contraction equation to find the velocity (v=c√(1-(25/65)^2) but when I plug that into the time dilation equation I don't get the correct answer. I get 25 when the answer should be 27. Where am I going wrong?
 
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persephoneia said:

Homework Statement


Suppose you decide to travel to a star 65 light-years away at a speed that tells you the distance is only 25 light-years. How many years would it take you to make the trip?

Homework Equations


∆t=∆t0/(√ (1−v2/c2 )) / ∆t0 = ∆t √(1−v2/c2)
L=L0√ (1−v2/c2)

The Attempt at a Solution


I've attempted to use the length contraction equation to find the velocity (v=c√(1-(25/65)^2) but when I plug that into the time dilation equation I don't get the correct answer. I get 25 when the answer should be 27. Where am I going wrong?

If you know the distance in your frame and the velocity in your frame, what do you need time dilation for?
 
PeroK said:
If you know the distance in your frame and the velocity in your frame, what do you need time dilation for?
I don't. I wasn't thinking that light years is also a distance because I looking at an example for the problem that combined the two equations (length contraction & time dilation) which threw me off. It's basically t=d/v after you figure out velocity right?
 
persephoneia said:
I don't. I wasn't thinking that light years is also a distance because I looking at an example for the problem that combined the two equations (length contraction & time dilation) which threw me off. It's basically t=d/v after you figure out velocity right?

Right!
 

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