Time dilation and length contraction at relativistic speeds

[riddledum]

Hi guys and girls. Need some assistance with these problems, not the hardest examples, but I need some help on the way.

Homework Statement

1.

An astronaut travels at 0.9c across our galaxy, which is 100 000 light years in diameter. How long time will it take (according to the astronaut) to travel from one end of the galaxy to the other?

2.

Same question, but in this question, the astronaut travels at 0.99c

3.

If the astronaut travels at 0.99c, he will perceive the length of the galaxy to another length, what is that length?

Homework Equations

L' = L*sqrt(1-v^2/c^2)

t' = t/sqrt(1-v^2/c^2)

 

[SammyS]

What have you tried?

Where are you stuck?

 

[riddledum]

As always, I have trouble getting started and getting my head around what to do and how. Some small tips to get started would be appreciated.

 

[riddledum]

Managed to solve both 2 and 3 now

 

[SammyS]

1. is just about like 2.

 

[riddledum]

What am I doing wrong here?


t' = t*sqrt(1-v^2/c^2)

t' = 100000*sqrt(1-0.9c^2/c^2)

t' = 31622.7766

 

[vela]

Where did you get t=100000 from? You also messed up crunching the numbers. Line 3 doesn't follow from line 2.

 

[riddledum]

Woops, saw what I did wrong there & Got the right answer immediately. Thanks a lot!