Time Dilation: 1.25yr Trip at 2.40x10^8m/s

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Discussion Overview

The discussion revolves around calculating the time experienced by an astronaut traveling at a high speed (2.40x10^8 m/s) relative to Earth, using the concept of time dilation from the theory of relativity. Participants explore the application of the time dilation formula and address issues related to calculations and assumptions.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant states that the trip took 1.25 years according to the astronaut's timing devices and seeks to find the duration as measured from Earth.
  • Another participant proposes that the answer is 2.08333 years, using the time dilation formula but presents it with a potential error in the equation.
  • Several participants discuss the correct form of the time dilation equation, with some suggesting the need to ensure that both velocity and the speed of light are in the same units.
  • There is confusion regarding the application of the formula, with one participant noting a negative square root when attempting calculations.
  • Another participant corrects the equation to use (v/c)^2 instead of (c/v)^2 and provides the correct values for v and c.
  • One participant expresses relief at finally understanding the calculation after multiple attempts and corrections from others.
  • A later post emphasizes the importance of careful calculation and understanding the process rather than rushing to find an answer.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the correct application of the time dilation formula initially, as there are multiple interpretations and corrections made throughout the discussion. However, there is a general agreement on the importance of careful calculation.

Contextual Notes

Participants express uncertainty about the correct form of the time dilation formula and the implications of unit consistency. There are unresolved issues regarding the calculations leading to negative results.

pmor@hotmail.
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An astronaut is traveling at a constant speed of 2.40x10^8 m/s relative to Earth through space. according to timing devices aboard the space vehicle the trip took 1.25 years. how long did the trip last if measured relative to earth
HELP PLEASE!
 
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I guess the answer is 2.08333 years.
1.25=x{1-(v/c)^2}^.5
x=2.08333
 
Last edited:
hemantc007 said:
I guess the answer is 2.08333 years.
1.25=x{1-(c/v)^2}^.5
x=2.08333

thats right!
but how did you get that?
do you need to convert the velocity?
 
pmor@hotmail. said:
thats right!
but how did you get that?
do you need to convert the velocity?

no you don't because , when we apply the formula (v/c)^2 both v and c are in same units i.e m/s...
 
Last edited:
hmm I am still not getting the right answer when i plug it into my calculator..
 
Set the calculator aside, write it out on paper first.
 
see the formula is t1 = t2 * { 1 - (v/c)^2 }^(1/2)
where t1 is time in space shuttle (at 2.4...velocity)
t2 is time measured on Earth
c is velocity of light
v is velocity of space ship
The above formula is time dilation formula ...
now try it again

ya you could do it on paper too, its easy calculation...
 
Last edited:
DaveC426913 said:
Set the calculator aside, write it out on paper first.

okay so it would be something like
1.25/ (1-(2.4x10^8)2)^(.5)
which gives me a negative square root
 
pmor@hotmail. said:
hmm I am still not getting the right answer when i plug it into my calculator..

The equation should be x= 1.25/{1-(v/c)^2}^(1/2) with (v/c) and not (c/v).

Use v= 2.40x10^8 m/s and c= 2.99792458x10^8 m/s and you should get the right answer.
 
  • #10
pmor@hotmail. said:
okay so it would be something like
1.25/ (1-(2.4x10^8)2)^(.5)
which gives me a negative square root

dude it is not v^2 ...but...it is v^2/c^2...
where c=299792458 m/s and
v is 2.4*10^8 m/s
 
Last edited:
  • #11
okay i got ittt finally
thanks guyyys
 
  • #12
The lesson here, I hope you see, is that, if you rush through the work just to get an answer, you're not paying attention. Setting aside the calculator forces you to ensure that the process leading up to the number at the end is the important part.
 
  • #13
pmor@hotmail.
I am sorry for that mistake i.e replacing c by v...
 

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