Find Relative SPEED of Image to Object: My Solution

[souro11]

This problem came in an exam .

An object is approaching a mirror with a SPEED V . Find the SPEED of the image relative to the object .

My solution - The object approaches the mirror with a SPEED V relative to the ground . Thus the image approaches the object with a SPEED V relative to the ground. Since this is SPEED , and NOT VELOCITY we don't give a damn to whether the image is traveling towards or away from the object , and in any case whatsoever the SPEED of the image relative to the object is going to be ZERO. However , if it has been velocity in case of speed , the relative velocity of the image w.r.t object would have been 2V.

Most people are saying the answer is 2V. Please enlighten .

 

[htg]

Speed is a scalar quantity, but it can have + or - sign.
You are interested in the quantity s-(-s) = 2s.

 

[Doc Al]

Since this is SPEED , and NOT VELOCITY we don't give a damn to whether the image is traveling towards or away from the object , and in any case whatsoever the SPEED of the image relative to the object is going to be ZERO. However , if it has been velocity in case of speed , the relative velocity of the image w.r.t object would have been 2V.

While you might only care about the magnitude of the answer (the speed), you are still adding velocities.

Consider this problem: A train is moving east at 50 mph. A person in the train throws a ball at 50 mph with respect to the train. What's the speed of the ball with respect to the ground? Would you not agree that it makes a difference whether the ball is thrown toward the east or toward the west?

 

[souro11]

While you might only care about the magnitude of the answer (the speed), you are still adding velocities.

Consider this problem: A train is moving east at 50 mph. A person in the train throws a ball at 50 mph with respect to the train. What's the speed of the ball with respect to the ground? Would you not agree that it makes a difference whether the ball is thrown toward the east or toward the west?

No! In both cases , whether the ball is thrown towards the east or west , the SPEED of the ball relative to the train is going to be 50 mph . Since the train is moving at a speed 50 mph w.r.t ground , the speed of the ball w.r.t ground in any case is going to be 50+50 = 100 mph . We are talking about speed , why should we be concerned about the direction ?

Let me give you an instance . Since we are taking uniform speed here , then at a particular instant , the ball is going to be at a SPEED of 50 mph relative to the train , regardless of whether it is thrown towards the east or towards the west or north or south.

 

[Doc Al]

In both cases , whether the ball is thrown towards the east or west , the SPEED of the ball relative to the train is going to be 50 mph .

That part's correct.

Since the train is moving at a speed 50 mph w.r.t ground , the speed of the ball w.r.t ground in any case is going to be 50+50 = 100 mph .

Wrong! If the ball is thrown in the same direction that the train is moving, then the speed of the ball w.r.t ground will be 100 mph. But if it's thrown in the opposite direction, the speed w.r.t ground will be zero!

We are talking about speed , why should we be concerned about the direction ?

Because, whether you realize it or not, you are adding velocities.

 

[GRDixon]

This problem came in an exam .

An object is approaching a mirror with a SPEED V . Find the SPEED of the image relative to the object .
Most people are saying the answer is 2V. Please enlighten .

This might be a trick question. The image actually exists at the mirror's surface; its apparent motion toward the object owes to our binocular vision. If it's a trick, then the speed relative to the object would be V, and its speed relative to the mirror would be zero.

 

[Doc Al]

The image actually exists at the mirror's surface;

The virtual image is behind the mirror, not at its surface.

 

[GRDixon]

The virtual image is behind the mirror, not at its surface.

" virtual image: an image (as seen in a plane mirror) formed of points from which divergent rays (as of light) seem to emanate without actually doing so" Merriam & Webster New Collegiate Dictionary. But like I suggested, it could be a trick question. My only other input is that speed is not relative; it is the magnitude of the velocity vector (which IS relative).

 

[Doc Al]

" virtual image: an image (as seen in a plane mirror) formed of points from which divergent rays (as of light) seem to emanate without actually doing so" Merriam & Webster New Collegiate Dictionary. But like I suggested, it could be a trick question.

You suggested that the image 'actually exists' on the surface of the mirror. I don't understand that statement. The mirror surface just reflects the light. (You're correct that the light doesn't really emanate from the location of the virtual image, but I think that's irrelevant.)

I doubt it's meant to be a trick question. At least not in a physics class.

My only other input is that speed is not relative; it is the magnitude of the velocity vector (which IS relative).

Why would you think speed is any less relative than velocity? To specify the speed, you need to specify relative to what.

 

[GRDixon]

I doubt it's meant to be a trick question. At least not in a physics class.

Why would you think speed is any less relative than velocity? To specify the speed, you need to specify relative to what.

Re trick questions: you're probably right. Physics is tough enough without trick questions. As for the relativity of speed, a stated velocity (3 components) specifies motion relative to a particular frame of reference. A stated speed can be the magnitude of each velocity in an infinite set of velocities.

 

[Doc Al]

A stated speed can be the magnitude of each velocity in an infinite set of velocities.

True, but even a speed must be relative to some reference frame.

 

[souro11]

We can never assign an algebric sign to speed . Hence we are interested in addition or subtraction of magnitudes from one another . When we are adding speed we are adding the magnitudes of the velocities WITHOUT putting any algebric sign in before them .

Thus in this specific problem , SPEED of the image relative to the object is going to be zero.

 

[Doc Al]

We can never assign an algebric sign to speed . Hence we are interested in addition or subtraction of magnitudes from one another . When we are adding speed we are adding the magnitudes of the velocities WITHOUT putting any algebric sign in before them .

Thus in this specific problem , SPEED of the image relative to the object is going to be zero.

Sorry, but that's nonsense. When you add or subtract you are actually dealing with velocities, since you are giving them signs. (That's where adding + or subtracting - come in!)

You can't just add speeds regardless of direction and expect to get a meaningful answer. Here's another example: Two cars each move at 50 mph. What's their speed relative to each other? Answer: Until you specify the directions they are moving in (in other words, their velocities) you cannot answer the question. If they move in opposite directions their relative speed will be 100 mph. (Which means they will approach or separate at that rate.) But if they move in the same direction, their relative speed is zero. That makes a huge difference, wouldn't you agree?

Given a velocity, speed is its magnitude and has no sign. But first you have to find the velocity, and that requires adding velocities.

 

[souro11]

Sorry, but that's nonsense. When you add or subtract you are actually dealing with velocities, since you are giving them signs. (That's where adding + or subtracting - come in!)

You can't just add speeds regardless of direction and expect to get a meaningful answer. Here's another example: Two cars each move at 50 mph. What's their speed relative to each other? Answer: Until you specify the directions they are moving in (in other words, their velocities) you cannot answer the question. If they move in opposite directions their relative speed will be 100 mph. (Which means they will approach or separate at that rate.) But if they move in the same direction, their relative speed is zero. That makes a huge difference, wouldn't you agree?

Given a velocity, speed is its magnitude and has no sign. But first you have to find the velocity, and that requires adding velocities.

No . Speed is the total distance covered in ANY direction divided by the time interval . It depends on only the distance covered ( which has no direction ) and time interval ( which again has no direction )

I just don't get why the hell do we need to get the velocities to get a speed ?

When we measure speed, we must consider some object (the one you are standing on, probably) to be at rest, and measure the speed of other objects relative to it - that is, as if it were at rest.

Take this example . Two cars are moving . One towards the East at 50 mph and the other towards the West at 50 mph , both measured relative to Earth . In any case , the speed of each of the vehicles , relative to Earth is 50 mph. This has no direction , and does not require finding out the velocity.

The same thing applies for their speeds relative to each other . When you are measuring speed w.r.t then are you considering the direction ? No. Then why should we consider the direction while measuring their speeds relative to each other ?

In the latter case , speed and velocities turn out to be vastly different , and might contradict common sense , but we do not require to consider direction when measuring speed. When scientists added the element of direction to speed , they got velocity .

Think unbiased , and reply . I'm sure you'll get what I mean.

 

[sagardip]

Listen Souro 11 I don't know from where you have developed such a great misconception about speed and velocity, but the answer to your question will be 2v ,the reason being simple that, the object covers vt distance in t seconds and the image too covers the same distance. So when we say relative to the object we mean the way the object will see the image coming towards itself.Therefore it appears to the object as if the image has traveled a distance 2vt towards him as because he considers himself to be at rest and hence the speed of the image relative to the object will be nothing but 2v.Thank You

 

[Doc Al]

Speed is the total distance covered in ANY direction divided by the time interval . It depends on only the distance covered ( which has no direction ) and time interval ( which again has no direction )

That's true, but it also depends on the reference frame you are using to measure the speed.

I just don't get why the hell do we need to get the velocities to get a speed ?

Whenever you are using speeds of some bodies relative to a frame to then compute their speeds relative to each other, you have to consider direction and thus velocity.

When we measure speed, we must consider some object (the one you are standing on, probably) to be at rest, and measure the speed of other objects relative to it - that is, as if it were at rest.

Exactly.

Take this example . Two cars are moving . One towards the East at 50 mph and the other towards the West at 50 mph , both measured relative to Earth . In any case , the speed of each of the vehicles , relative to Earth is 50 mph. This has no direction , and does not require finding out the velocity.

If all you care about is the speed of the cars with respect to the Earth, then you don't need to worry about velocity or direction. But if you care about the speed of the cars with respect to each other, then you do care about the direction in which they move.

The same thing applies for their speeds relative to each other . When you are measuring speed w.r.t then are you considering the direction ? No. Then why should we consider the direction while measuring their speeds relative to each other ?

Because you are using speeds relative to the earth to compute the speeds relative to each other. You must consider the directions in which they are moving!

As I stated previously, if the cars both travel east then their speed with respect to each other is zero! That means if the cars were 1 mile apart to begin with, they'll stay one mile apart. But if they travel towards each other--one going east and the other going west--their relative speed will be 100 mph. If they start out one mile apart, in 36 seconds they will crash into each other. I hope you will agree that that's quite a difference. Direction matters!

In the latter case , speed and velocities turn out to be vastly different , and might contradict common sense , but we do not require to consider direction when measuring speed. When scientists added the element of direction to speed , they got velocity .

In these examples, the speed is just the magnitude of the velocity.

Think unbiased , and reply . I'm sure you'll get what I mean.

You have some preconceived notions of speed versus velocity that are not quite correct. Open your mind and I'm sure you'll understand.

 

[souro11]

Well , I understand what you are saying . But then do you admit that Relative Speed is a misnomer or meaning less term ?

Actually this is supposed to be a trick question. So I thought maybe the trick was in the use of the term 'speed' . Let's see how it is corrected.

 

[Doc Al]

But then do you admit that Relative Speed is a misnomer or meaning less term ?

Not at all. Relative speed is a well-defined and useful term. (Although relative velocity is even more useful.)

Actually this is supposed to be a trick question. So I thought maybe the trick was in the use of the term 'speed' . Let's see how it is corrected.

Let us know.

 

[Dale]

I agree, relative speed is not a misnomer nor a trick concept. It is simply the magnitude of the relative velocity, as you would expect.