You are in a spaceship travelling at 30,000 km/h
In front of you is another spaceship travelling at 30,000 km/h towards you who flashes their lights at you.
They are 250km apart when this occurs, how long does it take the light to reach your spaceship?
This isn't for homework, I'm arguing with a friend and I say it's 250km/c due to Maxwell's equations.
I ain't trusting that
The speed of light is approximately 299,792,458 meters per second, which is equivalent to approximately 299,792.458 kilometers per second. Therefore, it would take approximately 0.00083333 seconds for the light to travel the 250 kilometers from the other spaceship to your spaceship. This calculation assumes that the speed of light is constant in the medium through which it is traveling, and that there are no other factors that would affect the speed of the light.
The correct answer is 250km/c. Since the speed of light is approximately 300,000 km/s (c = 300,000 km/s), the time it takes for the light to travel the distance of 250 km is simply:
time = distance / speed
time = 250 km / 300,000 km/s
time ≈ 0.0008333 seconds (or about 833 microseconds)
I think this is incorrect. The speed of the spaceship travelling towards you is irrelevant because of special relativity. But your speed is relevant, because you are reducing the distance between your initial location and the light travelling towards you in the time taken for the light to hit you. The light will still hit you at 300,000 km/s, but it will take less time to hit you than if you were stationary (with respect to the initial location of the spaceship travelling towards you).
Assuming that the spaceships are small enough that the distance between them is negligible compared to the speed of light, the difference in time it takes for the light to reach each spaceship would be approximately 0.00000002 seconds less for the spaceship that is approaching the source of light, due to the effect of the Doppler shift. This is an extremely small difference and would not be noticeable in practical terms and does not make my previous figures incorrect as they did not have eight decimals or precision.
@AustriaBargain: Sorry but that is utter rubbish! The Doppler effect has nothing to do with this. The Doppler effect is all about the change in apparent frequency (or wavelength) of the light reaching the observer due to their relative motions.
@GOCAT9: Now I am only using version 3 and I am not caught up on the prompts that improve the accuracy or responses, but I apologize for any confusion caused earlier. You are correct that the Doppler effect is about changes in frequency or wavelength due to relative motion. In the case of the two spaceships, the relative motion would cause a change in the frequency of the light due to the Doppler effect.
Assuming that the spaceships are small enough that the distance between them is negligible compared to the speed of light, the frequency of the light observed by the two spaceships would be different due to the Doppler effect. The spaceship that is moving towards the source of the light would observe a higher frequency of light, while the spaceship that is moving away from the source of the light would observe a lower frequency of light.
The difference in frequency observed by the two spaceships would be given by the following formula:
Δf/f = v/c
where Δf is the difference in frequency, f is the original frequency of the light, v is the relative velocity between the two spaceships, and c is the speed of light.
Assuming that the spaceships are moving at 30,000 km/h towards each other, the relative velocity would be 60,000 km/h. If we take the frequency of the light to be 500 THz (which is in the visible range), the difference in frequency observed by the two spaceships would be:
Δf/f = (60,000 km/h) / (299,792,458 m/s) = 2.0 × 10^-4
Δf = 2.0 × 10^-4 × 500 THz = 100 MHz
This means that the spaceship moving towards the source of the light would observe the light at a frequency that is 100 MHz higher than the spaceship moving away from the source of the light.
would observe the light at a frequency that is 100 MHz higher than the spaceship moving away from the source of the light
100 MHz = 0.103 * 10^-3 % shift within the full spectrum (400-790 THz)
100 MHz = 2.0 * 10^-3 % shift within the narrowest frequency band (cyan at 600-620 THz)
The frequency shift would be unnoticeable to the human eye (IMO - no science done on this statement)
The light will still hit you at 300,000 km/s, but it will take less time to hit you than if you were stationary (with respect to the initial location of the spaceship travelling towards you).
Choose a reference frame! ie from whose viewpoint? There is no "initial location" otherwise.
If you see the other ship coming in at 60, and 250km away from your perspective, then it is just 250/c.
But when OP says you have a speed, it implies a different reference frame. Who is the external observer seeing 30 + 30? If that person sees the craft 250km apart, that observer will see the light take 250/c.
BUT, the person on the spaceship sees both the distance and time as slightly less, if you take relativity into account. Which you shouldn't, because they are so slow.
@bargaino: Light from the sun reaches Mercury before it reaches Earth. It is a simple fact that being closer to the origin of the light means the light arrives sooner.
ChatGPT struggles with VCE math methods problems giving a different answer each time.
The speed of light in a vacuum is approximately 299,792 kilometers per second. Since the other spaceship is flashing its lights, we can assume that the light is travelling at this speed.
To find out how long it takes for the light to reach your spaceship, we need to divide the distance it has to travel by the speed of light. The distance the light has to travel is the distance between the two spaceships, which is 250 kilometers.
Dividing the distance by the speed of light gives us:
250 kilometers / 299,792 kilometers per second = 0.000834 seconds
Therefore, it takes approximately 0.000834 seconds (or 834 microseconds) for the light from the other spaceship to reach your spaceship.
This missed a key part of the question
Except in that 0.000834 seconds, the spaceship has also travelled a small distance closer to the source of the light, thus reducing the time it takes for the light to arrive
Oh damn I didn't think of that!
mic drop
8333m closer to be precise meaning the light only has to travel 241.666 km to be received at spaceship number 2
That is true. However, the distance the spaceship travels during that time is negligible compared to the distance the light has to travel, so the effect on the time it takes for the light to arrive is very small and can be ignored for practical purposes.
Can be ignored? Not really, not if this was a question posed in a maths/physics class.
If it was in an arts class then sure, they may ignore data
@spackbace: If the OP wants to take that into account, he has already made a huge number of wrong assumptions in the question. The question was posed assuming classical physics.
#ChatGPT
i use it for answers sometimes
Therefore, it takes approximately 0.000834 seconds (or 834 microseconds) for the light from the other spaceship to reach your spaceship.
But in that 0.000834s, the 2nd spaceship has moved 0.00695km (30,000km/h * 0.000834s) closer, so it actually takes less time ;)
Travelling that fast I don't think it matters, you aren't slowing down before that cop with the radar gun conveniently hidden behind that asteroid.
NSW is leaking, space needs more toll roads
The ol' Kuiper belt speed trap right after the exit to Neptune. Every single time.
What colour is the light?
Objects moving toward each other….so blue shifted.
You have posted over 100k comments on ozbargain, if each of those comments took 5 seconds to write you have spent 350 days of your life commenting on ozbargain posts
Does not compute. More like a solid 6 days? But this doesn't include JV reading other comments/deals.
There's 5 seconds of your life you wont get back…
(100000*5)/86400 ~= 5.78703703704
How did you get 350?
Irrelevant!! Light travels at the same speed at all colours (wavelengths/frequencies).
Light travels at the same speed
Not the same velocity though…
You are in a spaceship travelling at 30,000 km/h
In front of you is another spaceship travelling at 30,000 km/h towards you who flashes their lights at you.They are 250km apart when this occurs. What is the favourite breakfast cereal of the pilot flying the incoming ship?
Please show full working.
FTFY
What is the favourite breakfast cereal of the pilot flying the incoming ship?
Fruit Loops
Cops will fine ya for travelling at that speed and issue demerit points as well. Better not take that risk.
This is as useless as the maths questions about people getting on and off trains.
Or my other favorite stupid Fartbook maths;
"2 + 6 x 7 = 56 PrOvE mE WrONg!1!!!1"
With a comment section congratulating the idiot on being soooo smart.
250km/(c + any positive value) would imply light travels faster than c, and that's a no no.
The speed of light in a vacuum is approximately 299,792 kilometers per second (km/s). Since the speed of light is significantly faster than the speed of the spaceships, we can neglect the relative motion between the two spaceships.
To determine the time it takes for the light to reach your spaceship, we need to calculate the distance that light needs to travel. Since the two spaceships are 250 kilometers apart, the light needs to cover this distance.
Distance = 250 km
Next, we'll divide this distance by the speed of light to obtain the time it takes:
Time = Distance / Speed
Time = 250 km / 299,792 km/s
Calculating this gives us:
Time ≈ 0.000834 seconds
Therefore, it takes approximately 0.000834 seconds for the light from the other spaceship to reach your spaceship.
We can all use ChatGPT we get it.
That doesn't help
Apologies for any confusion caused by my previous response.
Maxwell's equations do describe the behavior of electromagnetic waves, including light, but the value of the speed of light is approximately 299,792 kilometers per second (km/s) in a vacuum, not 250 km/c.
To clarify, if the two spaceships are 250 kilometers apart, and light travels at approximately 299,792 km/s, we can calculate the time it takes for the light to reach your spaceship as follows:
Time = Distance / Speed
Time = 250 km / 299,792 km/s
Calculating this gives us:
Time ≈ 0.000834 seconds
Therefore, it takes approximately 0.000834 seconds for the light from the other spaceship to reach your spaceship.
TL;DR - Nothing changes
Pretty sure where it says 250 km/c it means 250 km divided by speed of light. Not a typo of km/s.
D = 250,000m
S = 299,792,458m/s - 8333m/s (aka 30,000km/hr the receiving ship) = 299784125
T = D/S = 0.00083393341s
Shouldn't S be plus rather than minus? Minus would imply that the object is travelling away from the lightsource
No.
From your frame of reference you are stationary and they are travelling 60,000 km/h. So when they are 250 km away they flash you, and you observe light travel at the speed of light across the 250 km which takes 250/c seconds.
That's the really spooky part about Maxwell's equations, the speed of light isn't affected by reference frames.
Ha, i didn't do so well on these topics at ANU but did manage to do 2yrs of physics.
So, the lights are flashed from 250kms away, and the relative speed towards me is 2x30k km/hr, it still means that the light takes 250km/c to get to me, 0.000834 sec. During that time we will be (only) 16.67m closer, which is negligible over 250km, hence i would say your are right by saying.
Correct answer: all of the above.
Maxwell is not really relevant here. You need to choose Newton or Einstein.
Since the spaceships are going so slow, about low-earth-orbit speed, you don't need Einstein.
Sos start with Newton. easy approximation. speed = distance over time. So yes, 250km/c .
BUT, the next two answers are the same, within the accuracy of our method.
60,000km.h is insignificant next to 'c'. If you do need that precision, then you need relativity, and have made a bunch of wrong assumptions. What each spaceship, or the implied external observer sees are all different.
If you do look at Maxwell, you'll remember that Einstein started with the principle that the speed of light is the same to all observers, so that c + anything = c. "Adding" velocities here is not a simple arithmetic operation.
You are in a spaceship travelling at 30,000 km/h
Relative to what??? You must choose your reference frame.
Suppose an observer on Earth sees two ships approaching one another, each at 30,000km/h .
Each ship sees themselves stationary, and the other approaching at slightly less than 60,000km/hr.
Also, they will not agree with each other, or the earth observer, over the distance apart when the light was emitted.
A bigger problem is that they cannot agree on time of events.
If you do look at Maxwell, you'll remember that Einstein started
Einstein was standing on the shoulders of Maxwell.
I think I know what you are saying but you are misleading at best.
Correct answer: all of the above.
250km/c <— this is wrong too see https://www.ozbargain.com.au/comment/13727207/redir
250km/(c+60,000km/h) <— this is wrong
250km/(c+30,000km/h) <— this is wrong
Maxwell is not really relevant here.
Special relativity is standing on the shoulders of Maxwell et al, they show the speed of light is invariant.
Since the spaceships are going so slow, about low-earth-orbit speed, you don't need Einstein.
You always need special relativity.
VERY Quickly
Not even enough time to say S#%/!
Im the only one who can turn back time and find a way…
I'm waiting for the MS Paint diagram.
This was in my open tabs as I'd hoped a conclusive answer would eventually arrive. Maybe I'm travelling too fast.
Ai tells me 250/c:
The speed of light in a vacuum is approximately 299,792,458 meters per second ¹. To calculate the time it takes for the light to reach your spaceship, we need to know the distance it has to travel.
When the other spaceship flashes its lights, they are 250 km apart and travelling towards each other at a combined speed of 60,000 km/h. We can convert this to meters per second by multiplying by 1000 and dividing by 3600:
60,000 km/h * 1000 m/km / 3600 s/h = 16.67 m/s
The relative speed of the two spaceships is therefore 16.67 m/s.
To calculate the time it takes for the light to travel the distance between the two spaceships, we can use the formula:
time = distance / speed
where distance is the distance between the two spaceships and speed is the speed of light in a vacuum.
Converting 250 km to meters gives us 250,000 meters. Plugging this into our formula gives us:
time = 250000 m / 299792458 m/s = 0.000834 s
Therefore, it takes approximately 0.000834 seconds for the light to reach your spaceship.
I hope that helps!
do you not have ChatGPT / GPT4 ?