Time Dilation Question (1 Viewer)

[js992]

A rocket is travelling to the star closest to earth, proxima centauri which is a distance of 4.3 light years away. The rocket travels at a speed of 0.8c and the time taken to accelerate and decelerate is negligible.
Calculate the number of years that will pass as measured by the crew of the rocket as they travel to Proxima Centauri.

a 3.2 years
b 4.3 years
c 5.4 years
d 7.2 years

What i did was
4.3/0.8 = 5.375
5.375 is the dilated time yes?

So subbing in the time dilation formula, i get 3.2, the proper time which is the time measured by the crew on the spacecraft.

So my answer is (a)
except, the answers say it's (c)

Have i done something wrong or is the answer wrong?

 

[MetroMattums]

The time should be shorter, unless the question is implying something else.

 

[js992]

My question is, is the answer A or C?

I got A

but the answers say C

 

[biopia]

What i did was
4.3/0.8 = 5.375
5.375 is the dilated time yes?

No, it's not... I think... lol

If you need to travel 2 km, and you walk at 0.5 km's an hour (slow... but bear with me), and you figure it will take you 4 hours to complete the journey, that is how long you will experience. It's maths, after all XD
If I was watching you do it, it would appear to me, being stationary, to take longer.

As per the above example, if the astronauts calculate how long their journey will take, they will come up with the same answer that you did... 5.375 ly. THAT is how long they will experience. People from earth will see the journey take longer than that.

This is why the answer is C.

It's a very tricky question XD It's one that you expect to have to use the equation, but then you don't!

I am not 100% sure, but I am pretty sure. I hope that helps, nonetheless.

 

[stampede]

A rocket is travelling to the star closest to earth, proxima centauri which is a distance of 4.3 light years away. The rocket travels at a speed of 0.8c and the time taken to accelerate and decelerate is negligible.
Calculate the number of years that will pass as measured by the crew of the rocket as they travel to Proxima Centauri.

a 3.2 years
b 4.3 years
c 5.4 years
d 7.2 years

What i did was
4.3/0.8 = 5.375
5.375 is the dilated time yes?

So subbing in the time dilation formula, i get 3.2, the proper time which is the time measured by the crew on the spacecraft.

So my answer is (a)
except, the answers say it's (c)

Have i done something wrong or is the answer wrong?

distance: 4.3 light years
speed: 0.8c

d=st
therefore t=d/s
therefore t=4.3/.8
therefore t = 5.375 which is approx. 5.4
thus, the answer is c.

trick q u see, theres no time dilation application here since the q says the frame of reference thats to be taken into account is the one with the astronauts in it, ie, on the rocket

tell me whether or not it hits you

 

[MetroMattums]

OH IGNORE WHAT I SAID BEFORE

I think the question is referring to the time taken in the astronaut's frame of reference - so the answer C is quite valid.

 

[js992]

Ok... but now i'll draw your attention to part 2 of the question..

Find the distance to proxima centauri measured by the crew on board.

The answer is 2.6 light years.

This means that, if they are travelling at 0.8c, they will measure a time of 2.6/0.8

which is 3.2 years.

Does this change your answer to the first part?

 

[stampede]

Ok... but now i'll draw your attention to part 2 of the question..

Find the distance to proxima centauri measured by the crew on board.

The answer is 2.6 light years.

This means that, if they are travelling at 0.8c, they will measure a time of 2.6/0.8

which is 3.2 years.

Does this change your answer to the first part?

no it doesnt change my answer to anything.

part 2: Find the distance to proxima centauri measured by the crew on board.

ok so, in their frame of reference, length is contracted, (while some1 on earth's f.o.r would explain it via time dilation)

so use the length contraction formula baby
sub in the numbers: answer = 4.3 x [( 1 - 0.8^2)^.5]
=2.58
=2.6

wassup

 

[Slowness]

Forgive me if i'm wrong but while going a certain speed, length may contract, but the distance stays the same. No matter how fast you go, the distance will still stay the same. It's the time over the distance that changes (time dilation) from different frames of reference.

Therefore it wouldn't be feasible to implement the length formula into this.

Again, forgive me if i'm wrong but ...

 

[stampede]

Forgive me if i'm wrong but while going a certain speed, length may contract, but the distance stays the same. No matter how fast you go, the distance will still stay the same. It's the time over the distance that changes (time dilation) from different frames of reference.

Therefore it wouldn't be feasible to implement the length formula into this.

Again, forgive me if i'm wrong but ...

nah mate, ur thinkin too deeply

"length may contract, but the distance stays the same."

this is bullshit, i will not forgive you. ever.

and it is feasible to implement the length formula into this, tis how the answer is generated. tell me specifically wats confusin you etc

 

[stampede]

oh lol, u think that distance is definite, like wat scientists pre einstein also believed.

the only thing that is definite and constant, is the speed of light c. distance time etc will all change based on different frames of references

 

[Slowness]

Rightio then.

I'll just look up a few references to confirm all facts.

I understand where you are coming from

Cheers


EDIT: AAAHH RIGHT!!!! From the astronauts Point of Reference, the 'distance' is moving back at 0.8C hence Dilation occurs which can be found through Length Dilation formulas

Cheers. thanks ofr clearing it up

 

[js992]

no it doesnt change my answer to anything.

part 2: Find the distance to proxima centauri measured by the crew on board.

ok so, in their frame of reference, length is contracted, (while some1 on earth's f.o.r would explain it via time dilation)

so use the length contraction formula baby
sub in the numbers: answer = 4.3 x [( 1 - 0.8^2)^.5]
=2.58
=2.6

wassup

Length contraction formula :
Contracted length = Proper length x (1-v^2/c^2)^0.5]

So you're saying 4.3 light years is the proper length, which is measured by someone on Earth.
Hence by using 4.3/0.8, the value of time found is from the person on Earth's perspective, hence dilated time ---> sub into time dilation formula-----> time measured by crew ----> answer a.

Correct me if im wrong in what i just said.