# Time Dilation, Spaceship Problem!

1. Jun 7, 2014

### Rookie

1. The problem statement, all variables and given/known data
A spaceship has traveled for 14 years at an average speed of 90% of the speed of light. Its round trip from Earth has taken 14 years according to clocks on the ship.

(a) How long has the journey taken according to Earth clocks?

2. Relevant equations
t = t’ / (1-v2/c2)-1/2

3. The attempt at a solution
I'm totally confused here, I think t' = v * differential of time
v = 90% of c
c = speed of light
But yeah, I need some clarity on what I'm doing here.
Any help would be appreciated!

2. Jun 7, 2014

### dauto

What's the difficulty? The problem gives you v and t' and asks for t. Just plug that into the formula you provided. Please try to learn how to use superscripts. It's not too hard and allows you write formulae correctly.

3. Jun 7, 2014

### dauto

No, t' = v * differential of time is not correct. t' is the time as measured by the ship's clock.

4. Jun 7, 2014

### Rookie

Hows this?
14 / (1 - 269 813 212 / 8.98755179 × 10^16) -1/2
= -0.5, which seems incorrect :|

5. Jun 7, 2014

### dauto

1st things 1st. The formula isn't t = t’ / (1-v2/c2)-1/2. It is t = t’ / (1-v2/c2)1/2, or better yet t = t’ / (1-(v/c)2)1/2

Last edited: Jun 7, 2014
6. Jun 7, 2014

### Rookie

t = t’ / (1-(v/c)2)1/2
t = 14 / ( (1 - ( 269813212.2 / 299792458)^2 )^1/2
t = 147.368421053
This looks more correct I think, could you check it out please.

7. Jun 7, 2014

### dauto

No, not t = t’ / (1-(v/c)2)1/2. The correct formula is t = t’ / (1-(v/c)2)1/2. You need to use the superscripts, seriously.

There is still something wrong with your calculation.

8. Jun 7, 2014

Why don't you suggest him Latex? It's easier than using s

9. Jun 7, 2014

### dauto

They are both easy.

10. Jun 7, 2014

Latex is more neat. You can't write something as beautiful as
$$\frac{t'}{\sqrt{1-(\frac{v}{c})^2)}}$$
using BBcodes

11. Jun 7, 2014

### micromass

Staff Emeritus
Or even better

$$\frac{t^\prime}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}$$

12. Jun 7, 2014

### Rookie

Okay so it's t = t’ / (1-(v/c)2)1/2, it's hard to do subscripts in quick post.
Can you tell me what part is wrong with my calculation, please?

13. Jun 7, 2014

### dauto

No doubt. All I want is for the equations to be correct. Neat is even better, of course, but not required. But being correct is required. How can people expect us to donate our time to answer their questions when they can't take the time to write a post that makes sense? It baffles me.

14. Jun 7, 2014

### Rookie

t = t’ / (1-(v/c)2)1/2
Is it 8.58395075279?

15. Jun 7, 2014

### Rookie

I'm new to physics, like really new. Some equations on the internet don't use sub-scripting when they mention it, so I haven't developed the habit of doing it yet. Sorry.
Also when I copy and paste the equation, sub-scripting gets removed.

16. Jun 7, 2014

### dauto

Use latex than. It's really easy.
I wish I could but I really don't know what you did wrong. Your result does not come from the expression. You're probably not using your calculator correctly. Try doing one step at a time instead of the whole expression and post that here that way we can figure where the problem is.

Last edited: Jun 7, 2014
17. Jun 7, 2014

### dauto

No, that's not right either.

18. Jun 7, 2014

### Rookie

Okay
t’ = 14
c = 299792458 m/s (speed of light)
average speed of 90% of the speed of light -
v = c * 0.9
v = 269813212 m/s
t = 14 / (1 - 269813212 / 299792458)2)1/2
14 / (1 - 269813212 / 299792458)2)1/2 = 73.6842105263
√73.6842105263 = 8.58395075279
t = 8.58395075279

Last edited: Jun 7, 2014
19. Jun 7, 2014

### dauto

Sorry but that calculation is wrong. You're making several mistakes. For instance, 14 / (1 - 269813212 / 299792458)2)1/2 = 73.6842105263 isn't correct at all. I still cant figure how you're getting those numbers but they are not correct.

20. Jun 7, 2014

### dauto

Seems like you're doing the operations in the wrong order. Please post it step by step.