Who will win this running race?

[TonyYuan]

TL;DR Summary

It was a running race between Newton and Einstein. I want to know who gets to the platform first.

Who will win this running race?

How many seconds are their scores?

 

[Ibix]

This looks like a homework question - so, what do you think and why?

Questions I'd ask before even starting:
- are the velocities meant to be velocity components?
- are those components measured in the Earth frame?
- are the 'score' times supposed to be measured in the Earth's rest frame, or proper times, or what?
Hopefully the question specifies all this, since it's rather ambiguous without.

 

[TonyYuan]

Hopefully the question specifies all this, since it's rather ambiguous without.

- are the velocities meant to be velocity components?
Yes, vx and vy.
- are those components measured in the Earth frame?
Yes.
- are the 'score' times supposed to be measured in the Earth's rest frame, or proper times, or what?
They are measured in the Earth's rest frame.

 

[Ibix]

Thank you for the clarification. What is your attempt at this question? PF rules require you to show some effort before we help you - our aim is for you to learn how to do this, not for us to get some practice in.

 

[TonyYuan]

I consulted some scholars and I got different answers, which surprised me because this physical scene is not complicated. There are many physicists here, so I hope I can get the right answer here. Thanks.

 

[PeroK]

I consulted some scholars and I got different answers, which surprised me because this physical scene is not complicated. There are many physicists here, so I hope I can get the right answer here. Thanks.

What is "velocity" anyway? How is it defined?

 

[TonyYuan]

What is "velocity" anyway? How is it defined?

velocity = speed + direction.
velocity is a vector and can be split or combined in any direction. The velocity of the spaceship here is split into the velocity in the x direction vx and the y direction vy.

 

[PeroK]

velocity = speed + direction.
velocity is a vector and can be split or combined in any direction. The velocity of the spaceship here is split into the velocity in the x direction vx and the y direction vy.

That's not a definition; that's a description. When you say $v_y$, how is that defined? What does $v_y = 0.2c$ mean?

 

[Ibix]

I consulted some scholars and I got different answers, which surprised me because this physical scene is not complicated. There are many physicists here, so I hope I can get the right answer here. Thanks.

If you asked the question as ambiguously as your original posting, I'm not surprised. It was open to interpretation and they probably interpreted it differently. Note that asking us does not help you - if you have five answers already and you ask us and we give you a sixth, are you any better off? If you're trying to decide the correct answer by popular vote instead of by showing your reasoning and talking it through with us, you will only get the right answer if you are lucky.

What answers did you get, and which one do you think is correct? @PeroK's response will help you to decide if you answer his question. (Edit - if you answer his second question correctly, I mean...

 

[TonyYuan]

That's not a definition; that's a description. When you say $v_y$, how is that defined? What does $v_y = 0.2c$ mean?

vy: The speed of the spacecraft relative to the Earth in the y direction.
vx:The speed of the spacecraft relative to the Earth in the x direction.

 

[PeroK]

vy: The speed of the spacecraft relative to the Earth in the y direction.
vx:The speed of the spacecraft relative to the Earth in the x direction.

And what is "speed"?

 

[Ibix]

And what is the definition of speed, without using the word "velocity" in your answer.

 

[TonyYuan]

And what is "speed"?

speed = Displacement/time

 

[PeroK]

speed = Displacement/time

Well, that's velocity, but anyway it proves the point. The y-component of velocity is, by definition, the y-displacement over time.

What can you conclude from this? Say, for example, that Einstein wins the race. What does that tell you about the y-components of velocity?

 

[TonyYuan]

Well, that's velocity, but anyway it proves the point. The y-component of velocity is, by definition, the y-displacement over time.

What can you conclude from this? Say, for example, that Einstein wins the race. What does that tell you about the y-components of velocity?

There are two well-known mathematical formulas in special relativity:
1.w = (u + x) / (1-u * x / c ^ 2)
2.t = sqrt (1-v ^ 2 / c ^ 2)
How do we apply it in this topic. This is also where I am sleepy, who actually arrived at the platform first.

 

[PeroK]

There are two well-known mathematical formulas in special relativity:
1.w = (u + x) / (1-u * x / c ^ 2)
2.t = sqrt (1-v ^ 2 / c ^ 2)
How do we apply it in this topic. This is also where I am sleepy, who actually arrived at the platform first.

What does special relativity have to do with this question?

 

[TonyYuan]

What does special relativity have to do with this question?

One scholar told me that the vertical velocity component is affected by the time factor.
rate = sqrt (1-v ^ 2 / c ^ 2), so relative to the earth, the speeds of the two spaceships have become
vy1 = 0.2c * rate1, rate1 = sqrt (1- (0.4c) ^ 2 / c ^ 2)
vy2 = 0.2c * rate2, rate2 = sqrt (1- (0.2c) ^ 2 / c ^ 2)
Then he told me that the distance was 10Ls, so the last one to arrive was the one with the smaller vx, which was Newton's first arrival. Do you think his answer is correct? I don't understand.

 

[PeroK]

One scholar told me that the vertical velocity component is affected by the time factor.
rate = sqrt (1-v ^ 2 / c ^ 2), so relative to the earth, the speeds of the two spaceships have become
vy1 = 0.2c * rate1, rate1 = sqrt (1- (0.4c) ^ 2 / c ^ 2)
vy2 = 0.2c * rate2, rate2 = sqrt (1- (0.2c) ^ 2 / c ^ 2)
Then he told me that the distance was 10Ls, so the last one to arrive was the one with the smaller vx, which was Newton's first arrival. Do you think his answer is correct? I don't understand.

As I said, this goes back to the definition of velocity. Your original diagram shows the velocity in the Earth frame- yes? It shows the distances in the Earth frame - yes? Time is going to be measured in the Earth frame- yes?

Either the y-velocity is $0.2c$ (in the Earth frame) or it isn't. If it is, then that's what you use. If it isn't then your data is wrong. If, let's say the y-velocity of Einstein is less than $0.2c$, then that's what you should have on your diagram. Surely?

Special Relativity only applies if you want to analyse the race in a different frame. Since you don't, any transformation of lengths, times and velocities is utterly irrelevant.

 

[TonyYuan]

As I said, this goes back to the definition of velocity. Your original diagram shows the velocity in the Earth frame- yes? It shows the distances in the Earth frame - yes? Time is going to be measured in the Earth frame- yes?

Either the y-velocity is $0.2c$ (in the Earth frame) or it isn't. If it is, then that's what you use. If it isn't then your data is wrong. If, let's say the y-velocity of Einstein is less than $0.2c$, then that's what you should have on your diagram. Surely?

Special Relativity only applies if you want to analyse the race in a different frame. Since you don't, any transformation of lengths, times and velocities is utterly irrelevant.

ok, this is another answer I got, it looks reasonable.
So as the platform's vision, who will first encounter platform?

 

[PeroK]

ok, this is another answer I got, it looks reasonable.
So as the platform's vision, who will first encounter platform?

It's a draw by definition of (component of) velocity. Two objects with the same y-component of velocity have the same y-displacement in the same time. By definition. Assuming all data applies to a single reference frame.

 

[TonyYuan]

"As I said, this goes back to the definition of velocity. Your original diagram shows the velocity in the Earth frame- yes? It shows the distances in the Earth frame - yes? Time is going to be measured in the Earth frame- yes? "
I think their speed relative to the Earth is definite, because I gave a clear reference, which is the earth. The moment they left the earth, the speed didn't change. If this premise does not hold, then we cannot conduct research.

 

[TonyYuan]

It's a draw by definition of (component of) velocity. Two objects with the same y-component of velocity have the same y-displacement in the same time. By definition. Assuming all data applies to a single reference frame.

The platform is stationary relative to the earth.

 

[A.T.]

The platform is stationary relative to the earth.

Then it has the same simultaneity.

 

[TonyYuan]

Then it has the same simultaneity.

ok, you mean they will reach the platform at the same time.
Newton thought the same way. I don't know if Einstein thought so too. There was an American astronomer who gave me the answer that they would not arrive at the same time. He has absolute authority in a scientific forum.

 

[A.T.]

ok, you mean they will reach the platform at the same time.

In the reference frame of the Earth and platform, were both start simultaneously with the same vertical velocity.

 

[Ibix]

ok, you mean they will reach the platform at the same time.
Newton thought the same way. I don't know if Einstein thought so too. There was an American astronomer who gave me the answer that they would not arrive at the same time. He has absolute authority in a scientific forum.

As A.T. points out, observers at rest or only moving parallel to y in the Earth frame (such as Earth and your platform) will regard this race as a draw. Observers with any motion in the x direction in the Earth frame (such as Newton and Einstein in your example) will get different results for who won.

It isn't clear from what you've said which frame your astronomer was using. He may have made a mistake, or interpreted your question differently, or he may be using a different frame from the one you think he is.

I must say that the use of Newton and Einstein as characters in this is potentially confusing. It isn't clear in your last sentence whether you refer to the historical figures and their theories or to the characters in your scenario.

 

[TonyYuan]

In the reference frame of the Earth and platform, were both start simultaneously with the same vertical velocity.

Can you answer this question：
What is the relative speed between AB? va and vb all relative to the earth.
Earth-----------------A---->
|-----------------------va=0.9c
|
|
\/ B vb=0.9c

 

[PeroK]

ok, you mean they will reach the platform at the same time.
Newton thought the same way. I don't know if Einstein thought so too. There was an American astronomer who gave me the answer that they would not arrive at the same time. He has absolute authority in a scientific forum.

Let's assume that Newton reaches the platform in $100s$ (Earth frame). He has traveled $20$ light seconds in the y-direction in $100s$. That's $0.2c$ for the velocity component in the y-direction. By definition.

Let's also assume that Einstein reaches the platform in $50s$ (Earth frame). He has traveled $20$ light seconds in the y-direction in $50s$. That's $0.4c$ in the y-direction.

That's what velocity and components of velocity mean. You calculate them by taking y-displacement over time. If Einstein does not reach the platform in $100s$, then the y-component of his velocity is not $0.2c$. There can be no argument about this.

 

[TonyYuan]

Let's assume that Newton reaches the platform in $100s$ (Earth frame). He has traveled $20$ light seconds in the y-direction in $100s$. That's $0.2c$ for the velocity component in the y-direction. By definition.

Let's also assume that Einstein reaches the platform in $50s$ (Earth frame). He has traveled $20$ light seconds in the y-direction in $50s$. That's $0.4c$ in the y-direction.

That's what velocity and components of velocity mean.

What is your basis for making 100s and 50s? Their velocity in the y direction relative to the Earth is the same, and their velocity in the x direction is different.

 

[Dale]

Summary:: It was a running race between Newton and Einstein. I want to know who gets to the platform first.

Who will win this running race?

View attachment 259882

How many seconds are their scores?

Please post homework type questions in the homework section. It is mandatory to use the template and, in particular, to show your work.

I consulted some scholars and I got different answers

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