Relative Motion: Understanding the Relationship Between Moving Objects

[MatinSAR]

Homework Statement

Suppose you are walking next to a flowing river. Is it possible for you to see that the river is still?

Relevant Equations

Relative motion.

My attemp :

$\vec r_1$ : Position of the river in reference frame.
$\vec r_2$ : Position of the walker in reference frame.
$\vec r_x$ : Position of the walker measured by the river.

We have: $$\vec r_1 + \vec r_x = \vec r_2$$ $$\vec v = \dfrac {d \vec r}{dt} $$ $$\vec v_1 + \vec v_x = \vec v_2$$ $$\vec v_x = \vec v_2 - \vec v_1$$
So if the river and the walker are moving is same direction with same speed then the walker sees that the river is still.

 

[Orodruin]

Did you have a question regarding this result?

 

[MatinSAR]

Did you have a question regarding this result?

I'm not familiar with relative motion so I'm not sure if my answer is right or wrong ...

I've seen a video and in that video the person who is filming a river is walking in opposite direction of the river and in her video the river is still. And this is why I think I am wrong.

 

[Ibix]

I've seen a video and in that video the person who is filming a river is walking in opposite direction of the river and in her video the river is still.

That's either wrong or you have misinterpreted what was said. Possibly it said something like "you subtract your velocity vector from the river's velocity vector" and hence displayed her velocity reversed.

Drop the maths for now. Imagine you are standing by a river that flows towards your right. Drop a stick in it. Which way does the stick move? Which way would you have to move so that the stick stays in front of you?

So if the river's velocity is $\vec v$, what velocity do you need to acquire?

 

[MatinSAR]

Drop the maths for now. Imagine you are standing by a river that flows towards your right. Drop a stick in it. Which way does the stick move? Which way would you have to move so that the stick stays in front of you?

Right direction.

So if the river's velocity is $\vec v$, what velocity do you need to acquire?

$\vec v$ of course ...

So ... The video was wrong?

 

[Orodruin]

So ... The video was wrong?

This is impossible to say. Unless you link the video we have no way of telling whether the video is wrong or if you misinterpreted it. This is why you should always provide your references.

 

[MatinSAR]

This is impossible to say. Unless you link the video we have no way of telling whether the video is wrong or if you misinterpreted it. This is why you should always provide your references.

I've tried to upload it but I couldn't. Can't we forget about the video? I just wanted ti know if my answer to the original question is right or wrong ...

 

[MatinSAR]

https://mega.nz/file/krtDFBYT#yO8Wc-UOsUrbTn4yPddMaHUd450IrfKzjwbOErqFTRc

That video ...

 

[kuruman]

Homework Statement: Suppose you are walking next to a flowing river. Is it possible for you to see that the river is still?

You intuitively know it is but you have to define exactly what you mean by "see that the river is still." Then it should be clear how to think about it.

Imagine that you are driving on a highway in a straight line and your speedometer reads 80 km/h. You look out your left window and see a car in the left lane also moving with a speedometer reading of 80 km/h. Although you see the wheels of the car spin, you also see that the car is "still". Furthermore, you observe that trees and houses are moving backwards at 80 km/h. What or who is "still"? That's a non-question unless you specify relative to what.

 

[Hill]

"River" is not a rigid body. It does not move all at one velocity. Different parts move with various speeds and in various directions.
On top of this, what you "see" is the water surface. It can move opposite to the river flow. It happens, e.g., at flood tide in vicinity of the river mouth.
Moreover, the water can move one direction but the waves on the surface pushed by wind can move in the opposite direction. So, one could walk up the river and "see" it being still.

 

[MatinSAR]

You intuitively know it is but you have to define exactly what you mean by "see that the river is still." Then it should be clear how to think about it.

By seeing that the river is still I meant relative to that person who is walking by the river.

Imagine that you are driving on a highway in a straight line and your speedometer reads 80 km/h. You look out your left window and see a car in the left lane also moving with a speedometer reading of 80 km/h. Although you see the wheels of the car spin, you also see that the car is "still".

It is still relative ro the driver.

Furthermore, you observe that trees and houses are moving backwards at 80 km/h. What or who is "still"?

They are moving relative to the driver.

That's a non-question unless you specify relative to what.

I meant that in what situation the river is still relative to the person who's walking next to it.
And in post #1 I tried to answer it.

 

[MatinSAR]

"River" is not a rigid body. It does not move all at one velocity. Different parts move with various speeds and in various directions.
On top of this, what you "see" is the water surface. It can move opposite to the river flow. It happens, e.g., at flood tide in vicinity of the river mouth.
Moreover, the water can move one direction but the waves on the surface pushed by wind can move in the opposite direction. So, one could walk up the river and "see" it being still.

Good point. We can assume that it is a rigid body in this question. I just wanted to learn about relative motion.

 

[Ibix]

So ... The video was wrong?

If it says what you say, yes. It's possible you've misread it, so it might be worth re-watching it with the correct answer in mind. Did you misunderstand it or is it wrong? Given your conclusion, do you want to trust it, and/or other videos in the series?

 

[phinds]

https://mega.nz/file/krtDFBYT#yO8Wc-UOsUrbTn4yPddMaHUd450IrfKzjwbOErqFTRc

That video ...

You are being misled. The video correctly says that it LOOKS like it is standing still when the car moves but that is because the motion of the viewpoint is changing. Yes, the driver of the car is moving the car in the opposite direction of the river but the river just keeps moving at the same rate opposite the direction of the car. When the car moves, the view LOOKS like the river has stopped, but it has not. This is a TERRIBLE example to use to show the relative motion of objects.

 

[MatinSAR]

If it says what you say, yes. It's possible you've misread it, so it might be worth re-watching it with the correct answer in mind. Did you misunderstand it or is it wrong? Given your conclusion, do you want to trust it, and/or other videos in the series?

I've watched it many times. That video is not the problem. I wanted to find the answer of my question in post #1. And I know the answer thanks to people who replied in this topic.

 

[MatinSAR]

You are being misled. The video correctly says that it LOOKS like it is standing still when the car moves but that is because the motion of the viewpoint is changing. Yes, the driver of the car is moving the car in the opposite direction of the river but the river just keeps moving at the same rate opposite the direction of the car. When the car moves, the view LOOKS like the river has stopped, but it has not. This is a TERRIBLE example to use to show the relative motion of objects.

I should forget the video completely...

 

[Hill]

I should forget the video completely...

Right. It is just an optical illusion.

 

[Steve4Physics]

In addition to what @phinds said, can I add this (since I'd already typed it!).

I didn’t observe what the commentator in the movie said.

The water-surface pattern moves right when the car is stationary and moves even faster to the right when the car moves left. This is exactly what you would expect.

I suspect that there is an optical illusion at play. When the car moves left, the vegetation in the near-foreground appears to move quickly to the right. The apparent motion of the water relative to the near-foreground vegetation deceives the brain.

Well, that’s my theory.

 

[MatinSAR]

The water-surface pattern moves right when the car is stationary and moves even faster to the right when the car moves left. This is exactly what you would expect.

That's what I think.

Well, that’s my theory.

Thanks for sharing.

Right. It is just an optical illusion.

Agree.

Thanks to everyone who helped with the question.

 

[haruspex]

https://mega.nz/file/krtDFBYT#yO8Wc-UOsUrbTn4yPddMaHUd450IrfKzjwbOErqFTRc

That video ...

As @Hill wrote, it is an optical illusion. The apparent motion of the river (partly through being further away) is slow compared with the motion of the foreground. The brain opts for the simplest interpretation, namely, that only the foreground is moving.
To see this, block out the foreground. You can then see that the motion of the river doesn't change.

 

[MatinSAR]

As @Hill wrote, it is an optical illusion. The apparent motion of the river (partly through being further away) is slow compared with the motion of the foreground. The brain opts for the simplest interpretation, namely, that only the foreground is moving.
To see this, block out the foreground. You can then see that the motion of the river doesn't change.

Thanks @haruspex ...

 

[kuruman]

Right. It is just an optical illusion.

When I was a child and looked up in the sky at the Moon while walking around in my neighborhood, I thought that the Moon was "following" me. After I learned some physics, I figured out that this was an illusion. The angular position of the trees a few meters away and houses a few tens of meters away relative to a fixed reference line, starting at my eyes and extending in my direction of motion, change continuously. By contrast, the angular position of the Moon (a few hundreds of kilometers away) relative to the reference line did not change. That created the illusion that the Moon following me.

We deduce that something is moving by comparing angular positions at different time intervals when the motion is across our line of sight. When the motion is towards or away from us, we are comparing its apparent angular size at different times. It's all perception of angles and how they change.

Now for the video. If you have to ascertain whether the water is "moving" you have to establish a fixed reference line of sight with respect to which you measure angular change of the water. This line always has one end at your eyes whether you are moving or not. Where is the other end? Obviously, a point on the ground which doesn't move. A convenient choice is a bush by the water's edge.

So here is how the illusion is formed (only my theory). When the camera is at rest relative to the ground, the angle between the reference line from your eyes to the bush and the line from your eyes to a point in the water changes. You deduce that the water is moving. When the camera moves in one direction and the water in the opposite direction with the more or less same angular speed about the bush, the bush remains in the straight line connecting your eyes to the point in the water. There is no angular change between the two lines and you deduce that the water is not moving.

 

[haruspex]

When the camera is at rest relative to the ground, the angle between the reference line from your eyes to the bush and the line from your eyes to a point in the water changes. You deduce that the water is moving. When the camera moves in one direction and the water in the opposite direction with the more or less same angular speed about the bush, the bush remains in the straight line connecting your eyes to the point in the water. There is no angular change between the two lines and you deduce that the water is not moving.

That only works for a point in the water at a particular distance. The illusion is that all the water freezes.

 

[Orodruin]

Isn’t it strange how the Sun doesn’t seem to move in the sky when you are driving? It must mean you are driving at the same speed as the Sun relative to Earth - just some 30 km/s … then again, maybe not …