8

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?

msiyer
  • 103
Manisha
  • 883

3 Answers3

7

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

Lagerbaer
  • 14,836
  • 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 05:45
  • please answer my question i am waiting for your concerned reply. – Manisha Feb 27 '12 at 05:50
  • @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
  • 1
    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 : http://en.wikipedia.org/wiki/Angular_velocity – anna v Feb 27 '12 at 16:24
  • Is it because the far away objects (which are visible from the earth) are massive. So an object with long radius looks really small from the earth. So it moves with great speed but we feel like it barely moves(It moves significantly, but it looks as if it moved by a small distance, from the earth) . (It is just like the diameter of that planet. Its diameter is really large but it looks really small for us) – Kaushik Sep 17 '19 at 19:32
0

Well thats because in any kind of general physics problem we consider a point object. While you travelling by train, you see nearer object to move faster than a far away object (say a tower) . What you should be actually seeing a a very tiny point on the nearer object and a very tiny point on the far away object. One more reason (which is a bit biological one) is that when you see a nearer object, you eyeballs tend to follow its position but it doesnt gets much time to follow that object as you are moving fast. However when you see a far away object, since its far from you, therefore it makes a very tiny angle with your eyeballs. Even though that tiny angle might mean a relative displacement of 10km (depending upon the distance of the object) .

Jdeep
  • 866
0

One way to explain it is using v=rω from circular motion. (I am assuming that both the objects move with equal velocity in your question.) Let's say 2 objects 1 and 2 are at a distance of r1 and r2 respectively, such that r2>r1 and are moving with velocity v in the direction perpendicular to which you are looking at, then you will be looking at their angular velocity (ω1 and ω2 respectively) now ω=vel./radius. Here r1 and r2 act as respective radii for obj. 1 and 2. Now ω1>ω2 because ω is inversely proportional to radius and obj.1 has a smaller radius than obj.2. As a result the object which is farther away from you appears slower.

M.A.P.
  • 53