Time Dilation Confusion :S (1 Viewer)

[bleh1234]

I'm confused with the working out in the Jacaranda textbook for this question:

If the person standing on the platform yawned just as the train was passing through, and this yawn lasted 2.000 as measured by the yawner, what would be the duration of the yawn as measured by the train travellers? (the train travellers are travelling at half the speed of light).

I assumed that t_v would be the 2s, and t_o would be the time as experienced by the travellers. However, the textbook did it the other way around and got 1.155s. Shouldn't the time be less since this is the moving frame?

So confused D: Please help!

 

[anomalousdecay]

The question is asking for what time relative to the train travellers was the yawn duration. So you have to remember that in this question the time of the travellers is the reference frame, t_v, and that the frame at rest, the frame that the yawn lasted for 2 seconds in, is the observed time frame, t_o.

Answer should be something like t_v = 2.309401... sec.

 

[bleh1234]

oh oops, i copied the wrong answer. Yes, that was the answer.
So just to confirm: t_v is the time measured by the train traveller because they are moving relative to the platform? And t_o is the observed time by the yawner because this is the rest frame where the yawn actually occurs?
Thanks a lot btw!

 

[anomalousdecay]

oh oops, i copied the wrong answer. Yes, that was the answer.
So just to confirm: t_v is the time measured by the train traveller because they are moving relative to the platform? And t_o is the observed time by the yawner because this is the rest frame where the yawn actually occurs?
Thanks a lot btw!

Yep. You just have to be really careful which one is said in the question to be the rest frame and which one is said to be the frame moving relatively to the other. Remember, you can make either frame the rest frame and either moving relative to the other. Just depends on which values you are given and where each value is coming from (is it coming from what is made the rest frame or the frame moving at relative velocity).

http://community.boredofstudies.org...lation-what-am-i-doing-wrong.html#post6911244

See that example and make a deduction from that as practice.

 

[IBEKEVINN]

The question is asking for what time relative to the train travellers was the yawn duration. So you have to remember that in this question the time of the travellers is the reference frame, t_v, and that the frame at rest, the frame that the yawn lasted for 2 seconds in, is the observed time frame, t_o.

Answer should be something like t_v = 2.309401... sec.

What you're implying is that the time aboard the ship (2.3 seconds) is larger than the outside observer time (2 seconds). This means that for every 2 seconds of outside observer time, 2.3 seconds would pass for the traveller. If this were scaled up i.e. 2 years has passed for the observer and 2.3 years have passed for the traveller - wouldn't this contradict the twin paradox where the traveller should have aged LESS then the observer (but instead has aged 2.3 years rather than 2 years)?