Space traveler and time dilation

[chenying]

Homework Statement

A space traveler takes off from Earth and moves at speed 0.81c toward the star Vega, which is 26 ly distant.

How much older will Earth observers calculate the traveler to be (according to her) when she reaches Vega than she was when she started the trip?

Homework Equations

t = t prime / sqr. root of (1 - v$$^{}2$$/c$$^{}2$$)

the v and the c are supposed to be squared.

The Attempt at a Solution

I used the above equation to first find the time that has elapsed in earth, which came out to be 32.0988 years.

Then i used that same number and set it as my t so i can find the amount of time again, since they asked for the age the Earth observers will see the traveler based on her age

 

[sylas]

Homework Statement

A space traveler takes off from Earth and moves at speed 0.81c toward the star Vega, which is 26 ly distant.

How much older will Earth observers calculate the traveler to be (according to her) when she reaches Vega than she was when she started the trip?

Homework Equations

t = t prime / sqr. root of (1 - v$$^{}2$$/c$$^{}2$$)

the v and the c are supposed to be squared.

The Attempt at a Solution

I used the above equation to first find the time that has elapsed in earth, which came out to be 32.0988 years.

Then i used that same number and set it as my t so i can find the amount of time again, since they asked for the age the Earth observers will see the traveler based on her age

When you use tex tags, put the whole equation inside the tags... like this. Click on the formula to see how it was typeset.
$$t = \frac{t'}{\sqrt{1 - v^2/c^2}}$$

What you've done sounds good. What did you get?

 

[chenying]

I got 54.7359 years, which was wrong. The wording of the question is really confusing and I do not know how to go about it.

 

[sylas]

I got 54.7359 years, which was wrong. The wording of the question is really confusing and I do not know how to go about it.

I think you have mixed up your t and t'. In the equation, t is elapsed time as measured by someone on Earth. t' is the elapsed time in the frame of the traveler

 

[chenying]

ok I understand that, but the wording of the question really confuses me. They want the how much older the woman is (based on her frame) but from their frame??

 

[sylas]

ok I understand that, but the wording of the question really confuses me. They want the how much older the woman is (based on her frame) but from their frame??

Not so much "based on her frame", but rather how much she herself has aged. You can calculate how much older she is in her own experience (that is, "according to her") in any frame you like. They all give the same answer for how much she herself has aged.

Cheers -- sylas