Calculating Light Speed and Time Dilation: A Guide to Relativity

[Dx]

Hi!

1) A fast spaceship is traveling with a speed of .80c. How fast would light travel from the headlights of the ship relative to a stationary observer?

I said the answer was .80c because there is no change, I mean on Earth sure it would be different because of the distance it had to travel right?


2) How fast should a moving clock travel if its to be observed by a stationary observer as running at 1/2 its normal rate?

How do I solve for this? I assume I must calculate the normal rate and take 1/2 of that, correct? But how do I find that answer??
dx

 

[quantumdude]

Originally posted by Dx
1) A fast spaceship is traveling with a speed of .80c. How fast would light travel from the headlights of the ship relative to a stationary observer?

I said the answer was .80c because there is no change, I mean on Earth sure it would be different because of the distance it had to travel right?

No, the answer is to be found in the postulates of relativity, which should have been among the first things discussed in that chapter.

2) How fast should a moving clock travel if its to be observed by a stationary observer as running at 1/2 its normal rate?

How do I solve for this? I assume I must calculate the normal rate and take 1/2 of that, correct? But how do I find that answer??

In your book, they must have worked out the phenomenon of time dilation. The formula must be there. Can you look it up and give it a shot?

 

[Dx]

Originally posted by Dx
1) A fast spaceship is traveling with a speed of .80c. How fast would light travel from the headlights of the ship relative to a stationary observer?

I said the answer was .80c because there is no change, I mean on Earth sure it would be different because of the distance it had to travel right?
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No, the answer is to be found in the postulates of relativity, which should have been among the first things discussed in that chapter.

Ok! the second postulate : light propagates thru empty space with a definte speed c independent of the speed of the source or observer. It also talks about If a person traveling toward or away from a source of light will measure the same speed for that light as someone at rest with respect to the source. So why do you say the answer is no, sir?

2) How fast should a moving clock travel if its to be observed by a stationary observer as running at 1/2 its normal rate?

How do I solve for this? I assume I must calculate the normal rate and take 1/2 of that, correct? But how do I find that answer??

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In your book, they must have worked out the phenomenon of time dilation. The formula must be there. Can you look it up and give it a shot?

Sorry I thought I had posted that formula anyways they gave me very little to work with. The numbers below are made up eg; [del]t and [squ]1 - v^2 / c^2) because these were not given in my question so how do I still solve for this?

t = [del]t / ( [squ]1 - v^2 / c^2)^1/2.
10s / ( [squ]1-.6)^2)^1/2 = 2.5x10^1

But I will definitely give it another try.

 

[quantumdude]

Originally posted by Dx
Ok! the second postulate : light propagates thru empty space with a definte speed c independent of the speed of the source or observer. It also talks about If a person traveling toward or away from a source of light will measure the same speed for that light as someone at rest with respect to the source. So why do you say the answer is no, sir?

Why do I say "no" to your answer of 0.8c?

Because the postulate says that light always travels at 1.0c!

Sorry I thought I had posted that formula anyways they gave me very little to work with.

They gave you everything you need. If one clock runs at 1/2 the rate of another, then it takes twice as long for the first clock to register the same amount of time. Say the "slow clock" ticks off t₀ seconds. Then the "fast clock" ticks off 2t₀ seconds (twice as many). The two times are related by the formula you posted, and the only unknown is the speed of the slow clock, which is what they ask for.

 

[Dx]

Originally posted by Tom
Why do I say "no" to your answer of 0.8c?

Because the postulate says that light always travels at 1.0c!



They gave you everything you need. If one clock runs at 1/2 the rate of another, then it takes twice as long for the first clock to register the same amount of time. Say the "slow clock" ticks off t₀ seconds. Then the "fast clock" ticks off 2t₀ seconds (twice as many). The two times are related by the formula you posted, and the only unknown is the speed of the slow clock, which is what they ask for.

Ok Tom! An easy question for you. Please tell me where in the postulate that I stated exactly from my physics book does it say anything about 1c. Are you going to try and explain to me; someone who has no experience but have been studying this chapter that its understood. Please, tell me that not your answer, Tom. I think you fail to realize here that the question may make sense to you but maybe not to me so why not give me the benefit of the doubt. Its not like, I am not trying hard here, I really am!
Dx

 

[quantumdude]

Originally posted by Dx
Please tell me where in the postulate that I stated exactly from my physics book does it say anything about 1c.

Dx, not only is it clearly stated in the postulate, but that is all the postulate says!

Here it is again, just as you wrote it:

light propagates thru empty space with a definte speed c independent of the speed of the source or observer.

Do you understand that c and 1c are exactly the same thing?

 

[Dx]

OK! But I still don't understand how that helps me I mean the answer is not .5c is it?

 

[quantumdude]

Originally posted by Dx
OK! But I still don't understand how that helps me I mean the answer is not .5c is it?

What does the postulate say?

 

[HallsofIvy]

Let me get this straight: you quote, and say you understand, a
postulate that says the speed of light is ALWAYS the SAME to EVERY observer, no matter what the motion and THEN you say you can't understand why the answer to the question "How fast would light travel from the headlights of the ship relative to a stationary observer?" is c rather than 0.8 c or 0.5 c ?

THE FUNDAMENTAL POSTULATE OF RELATIVITY (not a postulate in the mathematical sense- it's really based on experiment) say
that The speed of light is c TO ANY OBSERVER!