Relative Velocity of running towards a mirror

[Mech-Master]

If you are running towards a mirror at 5m/sec, at what speed is your reflection moving towards you?

 

[Danger]

Welcome to PF, Mech-Master.
Your reflection doesn't move at all. It's an artifact of the mirror, and hence is stationary.

 

[jtbell]

If you are running towards a mirror at 5m/sec, at what speed is your reflection moving towards you?

At what speed is the reflection moving towards the mirror, and in which direction? (To be specific, suppose you are running towards the left.)

 

[Mech-Master]

my reflection in the mirror will move towards me wouldn't it?(will move towards the mirror from the other side if you know what I mean haha)

i am not sure if it will move at the same speed (5m/sec)

or

if you run towards the mirror with the speed 5m/sec, your reflection runs towards the mirror at the same speed. However, Relative to you, you are stationary and the mirror is moving towards you at 5m/sec - so your reflection is moving towards you at 10 m/sec?I am not sure it's confusing

 

[Danger]

Okay, I got the meaning. Actually, I sort of assumed your meaning the first time, but went with the practical approach.
Your image will appear to approach at twice your speed—in this case, 10 m/s. In physical reality, it doesn't move at all. The easiest way to think of it is that as you take one step (let's say 1/2 metre) toward the mirror, your image seems to take one toward you at the same time. That gives an apparent distance closure of 1 metre.
Again, though, the image itself does not actually move forward or backward. The mirror is a fixed object, and the image is produced by it.

 

[jtbell]

the image itself does not actually move forward or backward.

If you are 2 m in front of the mirror, your image is 2 m behind the mirror. If you are 1 m in front of the mirror, your image is 1 m behind the mirror. In either case you can locate it geometrically using the law of reflection of light rays and some ray tracing and simple geometry. These distances have real physical implications. If you use a camera with manual focusing to take a picture of your own image in the mirror, you need to set the focusing control for a distance of 4 m or 2 m respectively.

When you change position, your image changes position, which I would consider to be "moving."

 

[Danger]

When you change position, your image changes position, which I would consider to be "moving."

You are far and away more educated than I, but I just can't agree with that. The image is merely a manipulation of light by a fixed object. Any 'movement' is essentially an illusion. Assuming that the mirror is incapable of motion, the image 'trapped within it' is equally motionless.
I'm not declaring that I'm correct, but that's the way that I see it. If you can clarify the situation, I'm always glad to be educated. (That might sound sarcastic, but that's not how it's intended.)

 

[Molydood]

It's slightly abstract but I don't have a problem with the image being seen as a moving object, defined by the distance traveled by the individual photons on their journey from the object to your eye (with a bounce off the mirror somewhere along the journey… this would be at half distance for the case of your eyeball, and approx half distance for other parts of your body)

 

[Danger]

That's my point, Molydood. Thanks for clarifying what I was thinking. The incoming photons stop at the mirror, not behind it. The emitted photons that compose the reflection originate at the mirror, not behind it. Any forward or backward movement is on an atomic scale.