Time Dilation, Spaceship Problem

In summary: Maybe you should ask someone more experienced?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.
  • #1
Rookie
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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!
 
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  • #2
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
No, t' = v * differential of time is not correct. t' is the time as measured by the ship's clock.
 
  • #4
Hows this?
14 / (1 - 269 813 212 / 8.98755179 × 10^16) -1/2
= -0.5, which seems incorrect :|
 
  • #5
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.
 
Last edited:
  • #6
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
Rookie said:
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.
 
  • #8
dauto said:
You need to use the superscripts, seriously.
Why don't you suggest him Latex? It's easier than using s
 
  • #9
adjacent said:
Why don't you suggest him Latex? It's easier than using s


They are both easy.
 
  • #10
dauto said:
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
 
  • #11
adjacent said:
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

$$\frac{t^\prime}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}$$
 
  • #12
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
adjacent said:
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.
 
  • #14
t = t’ / (1-(v/c)2)1/2
Is it 8.58395075279?
 
  • #15
dauto said:
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.
 
  • #16
Rookie said:
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.
 
Last edited:
  • #17
Rookie said:
t = t’ / (1-(v/c)2)1/2
Is it 8.58395075279?

No, that's not right either.
 
  • #18
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:
  • #19
Rookie said:
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.
 
  • #20
Seems like you're doing the operations in the wrong order. Please post it step by step.
 
  • #21
I think I got it right, if not I'll post step by step.
Is it 37.42?
 
  • #22
I think you calculated $$\sqrt{\frac{t^\prime}{1 - \left(\frac{v}{c}\right)^2}}$$ instead of
$$\frac{t^\prime}{\sqrt{1 - \left(\frac{v}{c}\right)^2}}$$
 
  • #23
Oh I think I did do that!
How about now: 19.9999998666?
 
  • #24
Wait ignore that gold on.
 
  • #25
Rookie said:
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
 
  • #26
Okay is it this: 4.42718873898?
 
  • #27
Rookie said:
Oh I think I did do that!
How about now: 19.9999998666?

Nope
 
  • #28
Rookie said:
Okay is it this: 4.42718873898?

Still nope
 
  • #29
:( it's about 3am and my mind tend to drift.
How about this 44.2718870949
 
  • #30
Go sit somewhere, relax and then do it Rookie. :smile:
 
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  • #31
Rookie said:
:( it's about 3am and my mind tend to drift.
How about this 44.2718870949

Still not it. Post it step by step.
 
  • #32
Okay, okay give me some time I'll be back with a new answer!
 
  • #33
t' / √1 - ( v / c )2

t' = 14
14 / √1 - ( v / c )2

14 / √ 1 - ( 269813212 / 299792458 )2
√ 1 - ( 269813212 / 299792458 )2
( 269813212 / 299792458 )2 =0.80999999879
14 / √ 1 - 0.80999999879
1 - 0.80999999879 = 0.19000000121
14 / √ 0.19000000121
√ 0.19000000121 = 0.43588989574
14 / 0.43588989574 = 32.1182026398
Answer = 32.1182026398

Please be right ;(
 
  • #34
Yes, now it is correct. Taking the time to solve the equation step by step can save you a lot of time and grief.
 
  • #35
So the answer is t=32.1 years. Don't forget the units and avoid excessive number of significant figures.
 
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<h2>1. What is time dilation?</h2><p>Time dilation is a phenomenon in which time appears to pass at different rates for objects moving at different speeds. It is a consequence of Einstein's theory of relativity and has been confirmed through various experiments and observations.</p><h2>2. How does time dilation affect space travel?</h2><p>Time dilation becomes significant when objects are moving at speeds close to the speed of light. This means that for astronauts traveling in a spaceship at high speeds, time will appear to pass slower for them compared to someone on Earth. This effect becomes more pronounced the faster the spaceship is traveling.</p><h2>3. Can time dilation be reversed?</h2><p>No, time dilation cannot be reversed. It is a fundamental aspect of the universe and is always present when objects are moving at high speeds. However, the effects of time dilation can be counteracted by accelerating or decelerating the spaceship, which can bring the astronauts back to the same time frame as those on Earth.</p><h2>4. How does time dilation impact GPS systems?</h2><p>GPS systems rely on precise timing to function correctly. Since satellites in the GPS system are moving at high speeds relative to Earth, time dilation causes their clocks to run slower. This must be accounted for in the GPS calculations in order to accurately determine location.</p><h2>5. Is time dilation the same as time travel?</h2><p>No, time dilation and time travel are two different concepts. Time dilation refers to the difference in the passage of time for objects moving at different speeds, while time travel involves the ability to move backwards or forwards in time. While time dilation can make it seem like time is passing at a different rate, it does not allow for actual time travel.</p>

1. What is time dilation?

Time dilation is a phenomenon in which time appears to pass at different rates for objects moving at different speeds. It is a consequence of Einstein's theory of relativity and has been confirmed through various experiments and observations.

2. How does time dilation affect space travel?

Time dilation becomes significant when objects are moving at speeds close to the speed of light. This means that for astronauts traveling in a spaceship at high speeds, time will appear to pass slower for them compared to someone on Earth. This effect becomes more pronounced the faster the spaceship is traveling.

3. Can time dilation be reversed?

No, time dilation cannot be reversed. It is a fundamental aspect of the universe and is always present when objects are moving at high speeds. However, the effects of time dilation can be counteracted by accelerating or decelerating the spaceship, which can bring the astronauts back to the same time frame as those on Earth.

4. How does time dilation impact GPS systems?

GPS systems rely on precise timing to function correctly. Since satellites in the GPS system are moving at high speeds relative to Earth, time dilation causes their clocks to run slower. This must be accounted for in the GPS calculations in order to accurately determine location.

5. Is time dilation the same as time travel?

No, time dilation and time travel are two different concepts. Time dilation refers to the difference in the passage of time for objects moving at different speeds, while time travel involves the ability to move backwards or forwards in time. While time dilation can make it seem like time is passing at a different rate, it does not allow for actual time travel.

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