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When we are in a moving train, nearby stationary objects appear to go backwards. In Physics, relative velocity can be employed to explain the phenomenon:

velocity of object w.r.t train = velocity of object - velocity of train

Far away stationary objects, however, appear to move slowly in comparison to nearby objects. Here the concept of relative velocity seems to fail. Why is it so? Does it mean that relative velocity formula is also dependent on the distance between the two objects?

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possible duplicate of Why do things that are far away seem smaller? –  Qmechanic Feb 27 '12 at 15:57

2 Answers 2

up vote 4 down vote accepted

It's because the angle under which a certain distance appears to you depends on how far away the object you are looking at is. I mada a diagram: One object is far away, one object is close. Traveling by the same distance, you see a large angle for the closer object and a small angle for the far object.Thus the angle grows slower for far away objects and thus it seems that you travel more slowly with respect to them.

enter image description here

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ok i got you what you mean to explain but answer me one more question then....Is the formula of relative velocity which i mentioned in my question is applicable only for nearby objects then.. –  Manisha Feb 27 '12 at 5:45
please answer my question i am waiting for your concerned reply. –  Manisha Feb 27 '12 at 5:50
@sanaya Please be patient. The transformation is correct. But if you see it from another perspective: Close by, you can only see objects of the size of a few meters. For objects far away you can recognize object of kilometers wide. This as to do with the same fewining angle, displayed so nicely in the picture above. –  Bernhard Feb 27 '12 at 12:51
I am very well convinced with the answer given above but then also there is only one doubt in my mind now ..Why the formula of relative velocity did not work here?please clear this doubt..your concerned answer will help me a lot.. –  Manisha Feb 27 '12 at 14:10
It is because velocity is dependent on meters/second but perception depends on the angles subtended. In the distance the eye is measuring angular velocity : en.wikipedia.org/wiki/Angular_velocity –  anna v Feb 27 '12 at 16:24

I also think the same.. The basic definition of relative velocity must be wrong.. I think relative velocity between two objects must be inversely proportional to the distance between them acting it to alter the dirxn..

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You should rephrase your thought. The inverse relation to the distance origins in simple trigonometry. Close train station fills the whole field of view and quickly is out of your maximal viewinh angle. Far away objects move a small angle. –  Stefan Bischof Mar 16 '13 at 13:57
Welcome to Physics.SE, kiranadhikari. Like the rest of the Stack Exchange network we use a questions and answer model here, not a threaded conversation model and there is not fixed ordering of posts. That means that phrases like "I also think the same.." are not very useful because the antecedent is not clear. On top of that "The basic definition of relative velocity must be wrong.." is a very strong claim as physicists and engineers have been using those definitions successfully for centuries. The concept that you may be looking for, "angular velocity", has also been known for centuries. –  dmckee Mar 16 '13 at 18:46
Thanks for your valuable suggestions. I am just new to this site. –  newera Mar 17 '13 at 12:06

protected by Qmechanic Oct 26 '13 at 16:35

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