Distance and your image on a mirror?

[graphicer89]

Distance and your image on a mirror??

1. Homework Statement

A) If you are 1 meter away from a plane mirror and approach the mirrow at 1 m/s, how long does it take you to reach your image?

B) At what speed do you approach your image if you walk towards a plane mirror at 1 m/s?Explain(Hint: the answer is not 1 m/s)



3. The Attempt at a Solution

A) I think its the obvious...it would take 1 second traveling at 1 m/s

B) This is where i don't even know where to start...All these is ,is a prep questions that i need to know how to do...please help me out...how to do B...

 

[Doc Al]

A) I think its the obvious...it would take 1 second traveling at 1 m/s

Good.

B) This is where i don't even know where to start

Hint: How far away is the image when you are 1 meter from the mirror?

 

[graphicer89]

Good.


Hint: How far away is the image when you are 1 meter from the mirror?

Well isn't the image 1 meter from the mirror so I am guessing it would take 2 seconds ?

 

[RoyalCat]

Well isn't the image 1 meter from the mirror so I am guessing it would take 2 seconds ?

I'd just like to start by saying I haven't studied optics, so what I'm saying is just my own intuition and logic, and I only have a reasonable certainty that I'm correct, since I don't know what EXACTLY a plane mirror is.
I'm assuming it is a regular mirror that just reflects everything, exactly as it is. That is to say, if I'm 1 meter away from it, I will see my reflection as though it were 1 meter away from the plane mirror, behind the mirror. Please correct me if I'm wrong, as that is my work assumption for this exercise.

I think that is incorrect.
For every meter you move towards your mirror image, your mirror image moves a meter towards you. Use relative velocity to find what your velocity relative to your mirror image is.

To help you get started, let's just lay out what the question gives us in terms of information:
[tex]v_{you-mirror}=1 m/s[/tex]
[tex]v_{reflection-mirror}=-1 m/s[/tex]

Now we want to find [tex]v_{you-reflection}[/tex]

If you are unfamiliar with the definitions of relative displacement/velocity/acceleration then please say so and I'll try and explain them to you, if you are though, then all you need is to apply the formula and you're done.

 

[Doc Al]

Well isn't the image 1 meter from the mirror so I am guessing it would take 2 seconds ?

How far is the image from you when you are 1 meter from the mirror?

Given the answer from part A, how does the distance between the image and you change in that 1 second it takes you to reach the mirror?

 

[graphicer89]

I'd just like to start by saying I haven't studied optics, so what I'm saying is just my own intuition and logic, and I only have a reasonable certainty that I'm correct, since I don't know what EXACTLY a plane mirror is.
I'm assuming it is a regular mirror that just reflects everything, exactly as it is. That is to say, if I'm 1 meter away from it, I will see my reflection as though it were 1 meter away from the plane mirror, behind the mirror. Please correct me if I'm wrong, as that is my work assumption for this exercise.

I think that is incorrect.
For every meter you move towards your mirror image, your mirror image moves a meter towards you. Use relative velocity to find what your velocity relative to your mirror image is.

To help you get started, let's just lay out what the question gives us in terms of information:
[tex]v_{you-mirror}=1 m/s[/tex]
[tex]v_{reflection-mirror}=-1 m/s[/tex]

Now we want to find [tex]v_{you-reflection}[/tex]

If you are unfamiliar with the definitions of relative displacement/velocity/acceleration then please say so and I'll try and explain them to you, if you are though, then all you need is to apply the formula and you're done.

Oh yea definitely I am self teaching my self physics and all that kinda made sense but not completely...how far is the image from you? well if its 1 meter from the mirror and I am 1 meter from the meter then its 2 meters away from me...so it would take me 2 seconds?

 

[Doc Al]

how far is the image from you? well if its 1 meter from the mirror and I am 1 meter from the meter then its 2 meters away from me...

Good.

so it would take me 2 seconds?

You already know the time it takes from part A.

(See my last post again; I added a few things.)

 

[graphicer89]

How far is the image from you when you are 1 meter from the mirror?

Given the answer from part A, how does the distance between the image and you change in that 1 second it takes you to reach the mirror?

Well i know its not 1 m/s because the hint says...its not 1 m/s ...you really got me thinking now...ok ...at what speed do you approach your image if you walk towards a plane mirror at 1 m/s...so then that means I am NOT APPROACHING the mirror at 2 M/s...

According to royalcat...My time to get to the mirror 1 m/s - the time the image gets to the mirror - 1 m/s = 1 m/s - -1 m/s = 2 m/s...i feel that i have the answer right in front of me but I am just not capturing it...i feel slow now...

 

[RoyalCat]

Well i know its not 1 m/s because the hint says...its not 1 m/s ...you really got me thinking now...ok ...at what speed do you approach your image if you walk towards a plane mirror at 1 m/s...so then that means I am NOT APPROACHING the mirror at 2 M/s...

According to royalcat...My time to get to the mirror 1 m/s - the time the image gets to the mirror - 1 m/s = 1 m/s - -1 m/s = 2 m/s...i feel that i have the answer right in front of me but I am just not capturing it

Heh, you're staggeringly close.
For every second you move towards the mirror plane, you get one meter close.
Your mirror image moves at the same rate you do, so for every meter you move towards the mirror plane, it does the same.

Your velocity relative to your mirror image is 2 m/s!

I'll see if I can upload a diagram to help you wrap your head around the concept of relative motion.

 

[Doc Al]

Well i know its not 1 m/s because the hint says...its not 1 m/s ...you really got me thinking now...ok ...at what speed do you approach your image if you walk towards a plane mirror at 1 m/s...so then that means I am NOT APPROACHING the mirror at 2 M/s...

Don't mix up distance or time with speed. It's easy. You're 1 meter away from the mirror; how far away is the image (from you)? When you reach the mirror, how far away is the image (from you)? How long did it take you to get to the mirror? How much distance (with respect to you) did the image appear to cover in that time? So what's the speed of the image with respect to you?

According to royalcat...My time to get to the mirror 1 m/s - the time the image gets to the mirror - 1 m/s = 1 m/s - -1 m/s = 2 m/s...i feel that i have the answer right in front of me but I am just not capturing it...i feel slow now...

Using relative velocity is perfectly fine. As long as you understand it.

 

[graphicer89]

Heh, you're staggeringly close.
For every second you move towards the mirror plane, you get one meter close.
Your mirror image moves at the same rate you do, so for every meter you move towards the mirror plane, it does the same.

Your velocity relative to your mirror image is 2 m/s!

I'll see if I can upload a diagram to help you wrap your head around the concept of relative motion.

So At what speed do you approach your image if you walk towards a plane mirror at 1 m/s?Explain(Hint: the answer is not 1 m/s)...its a 2 m/s because For every second you move towards the mirror plane, you get one meter close.Your mirror image moves at the same rate you do, so for every meter you move towards the mirror plane, it does the same.
...Is this right??

 

[graphicer89]

Don't mix up distance or time with speed. It's easy. You're 1 meter away from the mirror; how far away is the image (from you)? When you reach the mirror, how far away is the image (from you)? How long did it take you to get to the mirror? How much distance (with respect to you) did the image appear to cover in that time? So what's the speed of the image with respect to you?


Using relative velocity is perfectly fine. As long as you understand it.

Your right that's what was happening to me...if i am 1 meter from the mirror the image is 2 meters away from me...1 meter to the mirror and 1 meter to the image to the mirror...it took me 1 second ...it also took him 1 second to get to the mirror...he covered 1 m/s just like me...so then its 1 m/s? ...nope...i know the answer is not 1 m/s...so then it has to be 2 m/s...sorry if my scope of physics and my mind is really limited...

 

[Doc Al]

So At what speed do you approach your image if you walk towards a plane mirror at 1 m/s?Explain(Hint: the answer is not 1 m/s)...its a 2 m/s because For every second you move towards the mirror plane, you get one meter close.Your mirror image moves at the same rate you do, so for every meter you move towards the mirror plane, it does the same.
...Is this right??

Perfectly right.

Your right that's what was happening to me...if i am 1 meter from the mirror the image is 2 meters away from me...1 meter to the mirror and 1 meter to the image to the mirror...it took me 1 second ...it also took him 1 second to get to the mirror...he covered 1 m/s just like me...so then its 1 m/s? ...nope...i know the answer is not 1 m/s...so then it has to be 2 m/s...sorry if my scope of physics and my mind is really limited...

OK, but tighten up the reasoning. You start out 1 meter from the mirror: the image is 2 meters away. One second later, when your nose hits the mirror, the image is right on top of you--0 meters away. So in one second, the image traveled 2 meters with respect to you--thus the speed is 2 meters per second, or 2 m/s.

Make sense?

 

[graphicer89]

Perfectly right.


OK, but tighten up the reasoning. You start out 1 meter from the mirror: the image is 2 meters away. One second later, when your nose hits the mirror, the image is right on top of you--0 meters away. So in one second, the image traveled 2 meters with respect to you--thus the speed is 2 meters per second, or 2 m/s.

Make sense?

Oh when i started reading this i started laughing at how well obvious this is and why i couldn't get it ...and I am still laughing...yea really thanks so much...like i said I am self teaching my self physics and well i only have yall to depend on ...which I am about to finish this really soon..thanks so much...