# Solving SR: Time Dilation & Length Contraction - Planet to Ufo

• magicuniverse
In summary, a UFO travels from one planet to another, and according to observers on the left and right, it takes 1.83 and 2.69 seconds, respectively. The two planets are separated by a distance of 384,000 km.
magicuniverse

## Homework Statement

a ufo travels from one planet to another (distance measured 384000km) at v=0.8c.

1)How long does the trip take according to observer on planet left?

2)How long does the trip take according to observer in ufo?

3) What is the two planets distance measusured my aliens in the ufo?

## Homework Equations

I think I have to use the lorrentx transformations.

t'=alpha(u/c)(t-ux/c^2)

t=alpha(u/c)(t'+ux'/c^2)

x=alpha(u/c)(x'+u't)

## The Attempt at a Solution

This is my first ever SR question I have done. So I wasnt sure.

I thought that from the original planet the apparent velocity is going to be 0?

so i said the time takes was = 1.83 s?

So then i said using the above formula that alien man thought it would be = 2.69s

As this is wrong I havnt proceeded to the next part. Can you please tell me where i am going wrong and possibly give me some advice as to how to set up these types of questions.

thanks

come on surely someone can help me with this?

can someone tell me if I am posting this in the wrong place at least lol?

I can try to help. First, you should convert the distance in km to s, i.e. 384,000 km = ?s.
I used $$c = 3 * 10^8$$ and got d = 1.28s.

Now, I know that the aliens traveling in the ufo will have the shortest time. I used the spacetime equation

$$\Delta s^2 = \Delta t^2 - \Delta d^2$$

in this particular case, d = 0, (this has to do with the distance the 'clock' is from the person (or in this case alien) using the 'clock') I calculated t as distance/velocity so t = 1.6s (this is what I got for part B or 2 of your problem). Do you happen to know if this is the correct answer? If this is right, I may be able to get you to the first part.

Also, let me know if you're using a different value for c (such as 2.998).

magicuniverse said:
I thought that from the original planet the apparent velocity is going to be 0?
You are told that the ufo travels at 0.8 c.

so i said the time takes was = 1.83 s?
How did you arrive at this number?

Doc Al said:
You are told that the ufo travels at 0.8 c.

How did you arrive at this number?

kk so I know that speed =distance/time

so time = distance/speed = 4.8 seconds. Is that right?

magicuniverse said:
kk so I know that speed =distance/time
Good.

so time = distance/speed = 4.8 seconds. Is that right?
No. What's the distance? What's the speed?

No. What's the distance? What's the speed?

the distacne is 384000000m
and speed is 0.8*3ee9

when i put this into my calulator i get 1.6

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magicuniverse said:
also by plugging the numbers in i get the other time to be 8.00s. Is this right?
Don't worry about the time according to the ufo until you've nailed down the time according to the planet.

and for the other time i get 2.67s is that right?

magicuniverse said:
when i put this into my calulator i get 1.6
That's better.

magicuniverse said:
and for the other time i get 2.67s is that right?
Will the time for the trip as measured by the ufo be shorter or longer? By what factor? (Hint: The ufo can be treated as a single moving clock.)

Do moving clocks run slow or fast?

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Doc Al said:
That's better.

Will the time for the trip as measured by the ufo be shorter or longer? By what factor? (Hint: The ufo can be treated as a single moving clock.)

Simply from the twins paradox thing I am going to say that the time is shorter for the moving ufo.
So the time will be 1.25s right?

magicuniverse said:
Simply from the twins paradox thing I am going to say that the time is shorter for the moving ufo.
What you need is the formula for the time dilation of a moving clock. But yes, the moving ufo clock runs slow (according to the planet clocks)--so the time measured by the ufo will be shorter than that measured by the planet.
So the time will be 1.25s right?
How did you get this number?

Doc Al said:
What you need is the formula for the time dilation of a moving clock. But yes, the moving ufo clock runs slow (according to the planet clocks)--so the time measured by the ufo will be shorter than that measured by the planet.

How did you get this number?

I plugged numbers into a fomula in my book.

magicuniverse said:
I plugged numbers into a fomula in my book.
What formula?

t' = (t-ux/c^2)/root(1+u^2/c^2)

is it wrong?

magicuniverse said:
t' = (t-ux/c^2)/root(1+u^2/c^2)

is it wrong?
That's one of the Lorentz transforms, but with a typo. Here's the corrected version:
$$\Delta t' = \gamma(\Delta t - v\Delta x/c^2)$$

Where:
$$\gamma = \frac{1}{\sqrt{1 - v^2/c^2}}$$

But even simpler is to recognize that moving clocks run slow by a factor of $\gamma$:
$$\Delta T = \gamma \Delta T_0$$

(Either way will work.)

but putting all the numbers into the formula you gave me gives 2.67s? what am i doing wrong?

magicuniverse said:
but putting all the numbers into the formula you gave me gives 2.67s? what am i doing wrong?
I gave two formulas. Which one are you using? (Not that it matters--both will give the same answer.)

Looks to me like you are somehow reversing the primed and unprimed coordinates. What are you plugging in for $\Delta t$ and $\Delta x$? What do you get for $\gamma$?

i get 5/3 for lambda. is that wrong?

no sorry I am lying i get lambda to be 0.6 so t =0.96s is this right?

and i also get the distance to be 2.09m is that correct?

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magicuniverse said:
i get 5/3 for lambda. is that wrong?
You mean gamma, not lambda. That's correct.
magicuniverse said:
no sorry I am lying i get lambda to be 0.6 so t =0.96s is this right?
Gamma is always greater than 1; but, yes, that time is correct.

and i also get the distance to be 2.09m is that correct?
Redo that calculation.

## 1. What is time dilation and length contraction?

Time dilation and length contraction are concepts in Einstein's theory of relativity. Time dilation refers to the slowing down of time for an object that is moving at high speeds, while length contraction refers to the shortening of an object's length in the direction of its motion.

## 2. How does time dilation and length contraction affect travel to distant planets?

As an object travels at high speeds, time dilation and length contraction occur, making time appear to pass slower and distances appear shorter. This means that a traveler on a spaceship will experience time differently and may age slower compared to someone on Earth. Additionally, the length of the spaceship will appear shorter, allowing for faster travel to distant planets.

## 3. How does time dilation and length contraction relate to the speed of light?

According to Einstein's theory of relativity, the speed of light is the only constant in the universe. As an object approaches the speed of light, time dilation and length contraction become more significant. At the speed of light, time would stand still and length would shrink to zero.

## 4. Can time dilation and length contraction be observed in everyday life?

While time dilation and length contraction are significant at high speeds, they are not noticeable in everyday life. The effects only become apparent at speeds close to the speed of light.

## 5. How does time dilation and length contraction impact our understanding of the universe?

Time dilation and length contraction are essential concepts in understanding the behavior of objects in the universe. They help explain phenomena such as the slowing down of time in gravitational fields and the ability to travel to distant planets in a relatively short amount of time. Without these concepts, our understanding of the universe would be limited.

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