SR Homework problem. Help?



06122013, 08:52 PM




SR Homework problem. Help?
I need help from a physicist. My prof won't answer his email. He's out of the office till Wednesday. Here's the question:
Two stars are 70 light years apart. How fast does a spaceship need to travel for the astronauts inside to have aged 75 years? Problem is I don't know how long this takes in the inertial reference frame, or how far it seems to the travelers. If I knew I could easily find the velocity. Any hints? I just need the setup, I've tried the formula for time dilation and it isn't working out right. 

06122013, 10:55 PM




RE: SR Homework problem. Help?
I'm not a physicist and I am rank amateur at the maths, and haven't actually studied maths for about 18 years. Nevertheless, I'm interested in this topic so I'll give it a go based on [1]. Let the stars be in the rest frame and the space ship be in the "moving" frame. I'll use years and light years to avoid the c terms.
t' = gamma (t  vx) x' = gamma (x  vt) where gamma = 1/sqrt(1v^2). The same is true in reverse (with the velocity switched to negative to reflect our changed perspective), so: t = gamma (t' + vx') x = gamma (x' + vt') gamma has the same value in this frame because the squared v term loses the sign of v. We have x=70ly and t' = 75y. Therefore we have the following simultaneous equations: (1) 75 = gamma(t  70v) = (t  70v) / sqrt(1v^2) (2) x' = gamma(70  vt) = (70  vt) / sqrt(1v^2) (3) t = gamma(75 + vx') = (75 + vx') / sqrt(1v^2) (4) 70 = gamma(x' + 75t) = (x' + 75t) / sqrt(1v^2) Solve for v. Easy, right? Hrrm. Maybe the way to look at it is in terms of a spacetime diagram with a t'=75 line that intercepts the x=70 line and solve for v that way? [1] http://en.wikipedia.org/wiki/Lorentz_tra...figuration Give me your argument in the form of a published paper, and then we can start to talk. 

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08122013, 01:41 PM




RE: SR Homework problem. Help?
Physics teachers may now beat me. It was a units issue I was having. I was entering my distance in light years and my time in years, but was entering my c value in meters per second.
I am ready to accept the dunce hat. 

08122013, 05:40 PM




RE: SR Homework problem. Help?
Do you feel like presenting your answer on the forum?
Give me your argument in the form of a published paper, and then we can start to talk. 

08122013, 06:56 PM




RE: SR Homework problem. Help?
(08122013 01:41 PM)natachan Wrote: Physics teachers may now beat me. It was a units issue I was having. I was entering my distance in light years and my time in years, but was entering my c value in meters per second. I can totally picture a bunch of physics students huddled around a watercooler telling jokes in this fashion. 

09122013, 06:16 AM




RE: SR Homework problem. Help?
.683c
I know that t'=t/gamma and x'=x/gamma. velocity is equal to x/t, or x'/t'. It will be the same either way. t=t'*gamma. v=x/t'*gamma. Gamma is 1 divided by the square root of 1 minus v squared. solve for V. 



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