Time Dilation, Spaceship Problem

[Rookie]

Homework Statement

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?

Homework Equations

t = t’ / (1-v2/c2)-1/2

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!

 

[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.

 

[dauto]

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

 

[Rookie]

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

 

[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

2nd, you made some mistake with your calculator. Try again.

 

[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.

 

[dauto]

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.

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.

 

[adjacent]

You need to use the superscripts, seriously.

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

 

[dauto]

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

^{They are both easy.}

 

[adjacent]

They are both easy.

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

 

[micromass]

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

Or even better

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

 

[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?

 

[dauto]

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

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.

 

[Rookie]

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

 

[Rookie]

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.

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.

 

[dauto]

Okay so it's t = t’ / (1-(v/c)²)^1/2, it's hard to do subscripts in quick post.

Use latex than. It's really easy.

Can you tell me what part is wrong with my calculation, please?

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.

 

[dauto]

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

No, that's not right either.

 

[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

 

[dauto]

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

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 can't figure how you're getting those numbers but they are not correct.

 

[dauto]

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

 

[Rookie]

I think I got it right, if not I'll post step by step.
Is it 37.42?

 

[dauto]

I think you calculated $$\sqrt{\frac{t^\prime}{1 - \left(\frac{v}{c}\right)^2}}$$ instead of
$$\frac{t^\prime}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}$$

 

[Rookie]

Oh I think I did do that!
How about now: 19.9999998666?

 

[Rookie]

Wait ignore that gold on.

 

[dauto]

I think I got it right, if not I'll post step by step.
Is it 37.42?

Still not right. How many different ways can you do that wrong?
You need to review how to use your calculator

 

[Rookie]

Okay is it this: 4.42718873898?

 

[dauto]

Oh I think I did do that!
How about now: 19.9999998666?

Nope

 

[dauto]

Okay is it this: 4.42718873898?

Still nope

 

[Rookie]

:( it's about 3am and my mind tend to drift.
How about this 44.2718870949

 

[adjacent]

Go sit somewhere, relax and then do it Rookie.