Calculating the Time Difference in Special Relativity: Alphonse's Joy Ride

[Curious&TheNon]

Homework Statement

Alphonse decides to go for a joy ride in his Astro-Scooter. He maintains a speed of 0.604 c and is gone for 6.53 years according to his ship's clock. His twin brother Carl says he is full of beans. According to Carl, how long has Alphonse been gone?
To=?
T=6.53 years?
v=0.604c
c=3*10^8

Homework Equations

T= To/ (Sqrt of (1- v^2 / c^2)

The Attempt at a Solution

So first i noticed i had to convert the years into seconds because the other variables were in seconds (m/s). So i multiplied 6.53 by 365*24*60*60 to make it into seconds (205930080sec). Which then i plugged it into the formula as T. As for the velocity and the speed of light, the "c" cancels out because the velocity it measured by a fraction of the speed of light so then it would only look like this Sqrt of (1-0.604^2 ) for the denominator. I then multiplied the "T" by the denominator of "To" to get To by itself. The answer came out to be 164123044 seconds however i still got it wrong. Then i tried the other way where this time "T" was To , which came out to be 2583866150.5 seconds but still wrong, I am not sure which variable is right and what i mis calculated. Help is appreciated thank you :)

 

[arpon]

Look, $\frac{v^2} { c^2}$ is just a ratio. So you need not change the unit in this problem.

 

[Curious&TheNon]

Look, $\frac{v^2} { c^2}$ is just a ratio. So you need not change the unit in this problem.

My online assignment doesn't accept years as a unit though, only hours, minutes and seconds :/

 

[haruspex]

2583866150.5

Is that exactly what you entered? You seem to have an extra digit in there.

 

[Curious&TheNon]

Is that exactly what you entered? You seem to have an extra digit in there.

No not exactly i had to put it in sig figs which was three, so it came out to be 2.58E9. Ignore the extra digit my bad X)

 

[Curious&TheNon]

No not exactly i had to put it in sig figs which was three, so it came out to be 2.58E9. Ignore the extra digit my bad X)

I wouldn't have affect the answer anyways

 

[haruspex]

I wouldn't have affect the answer anyways

It would, since what you first posted was 10 times too much.

 

[Curious&TheNon]

Oh, thought you were talking about the decimal place, my bad. Anyways got 258386615.5 , just tried entering it again, however still wrong :/ Thanks for the header though! :)

 

[Curious&TheNon]

Oh, thought you were talking about the decimal place, my bad. Anyways got 258386615.5 , just tried entering it again, however still wrong :/ Thanks for the header though! :) that was probably a typo x)

 

[haruspex]

Oh, thought you were talking about the decimal place, my bad. Anyways got 258386615.5 , just tried entering it again, however still wrong :/ Thanks for the header though! :)

Then I'm stumped. 2.58E9 seconds looks right to me. Maybe... if you allow a year as 365.25 days, it just tips over to 2.59E9.

 

[Curious&TheNon]

Then I'm stumped. 2.58E9 seconds looks right to me. Maybe... if you allow a year as 365.25 days, it just tips over to 2.59E9.

Yeah still wrong dam i guess ill just ask my physics teacher about it this coming tuesday ill keep you posted hahaha thanks anyways though! :)

 

[Curious&TheNon]

Turns out the online assignment didnt mention they took years, so my physics teacher forgot to mention he customized the answer to accept it in years as well. Problem solved thanks!

 

[haruspex]

Turns out the online assignment didnt mention they took years, so my physics teacher forgot to mention he customized the answer to accept it in years as well. Problem solved thanks!

Thanks for letting me know.