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Scenario:

Two vehicles pass each other on a highway moving at 100km's an hour; from a stationary position beside the road you witness these cars pass each-other directly in front of you: from your perspective these cars are moving at 100km's an hour.

My Question: If you were inside either one of the 2 cars, looking straight out the window to where the other car would cross, would you perceive the vehicle to be moving at 200km's an hour as it passed you- due to both cars moving at 100km's in opposite directions?

I'm unsure if thats right or not- whenever I personally travel by car and bare-witness to another vehicle pass my window in the opposite direction at the same speed, it seems to always be moving much faster than it really is, assuming it was only because of the speed I was going when passing it.

Is this correct?

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  • $\begingroup$ Yes :-) but if you indicated why this is a question at all for you, better-quality answers would pour in $\endgroup$ – TheBlastOne Aug 28 '14 at 11:11
  • $\begingroup$ I guess it would! I was curious as to whether or not the vehicle passing would actually be perceived moving at such a speed- it seemed to me as wrong. $\endgroup$ – Harry David Aug 28 '14 at 11:24
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Rough impressions can be misleading. The other car really is moving 200 km/h from your point of view.

One thing to keep in mind is that you tend to perceive motion more readily when it is closer to you. This is at least partly due to the fact that you really only can see angular speed across your field of view (like degrees per second). To convert this into an actual speed, you need a sense of distance to the object in question, which you only have for nearby things where for example parallax kicks in.

As a result, if you are moving at 200 km/h, a stopped car right next to you will appear to be moving very fast, whereas the distant scenery off to the side won't, even though both are moving relative to you at the same speed.

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  • $\begingroup$ In fact the distant scenery will be moving at half the speed of the other car, relative to you, no? $\endgroup$ – gj255 Aug 28 '14 at 12:16
  • $\begingroup$ Indeed it would be: the scenery would be moving at the same speed as you (from your perspective of course.) The other car would also see the same as you too except on the opposite side of the road. $\endgroup$ – Harry David Aug 29 '14 at 10:12
  • $\begingroup$ @gj255 I worded that confusingly. I mean that even scenery passing by at a full 200 km/h doesn't look to be moving so fast. $\endgroup$ – user10851 Aug 29 '14 at 10:15
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Your understanding is correct. And switching between different perspectives (what physicists would call different inertial frames of reference) like that is a very useful tool in physics, because it turns out that the laws of physics have the same form no matter which inertial frame of reference a problem is described in. For more information, see https://en.wikipedia.org/wiki/Galilean_relativity .

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Yes you would actualy see the car with its speed added with your speed.

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    $\begingroup$ Hi Chris Ger, and welcome to Physics.SE! We like our answers to present some physical reasoning why their answer is correct instead of stating it in a one-liner. Please consider improving this answer in a way that someone reading it might learn something from it. Otherwise, have fun! $\endgroup$ – ACuriousMind♦ Aug 28 '14 at 14:57
  • $\begingroup$ This is not entirely correct. You would see its speed added to your speed using the relativistic velocity addition formula, which for two cars at 100km/h each translates to you seeing the other car travelling at 199.999999999998282947444..... km/h towards you $\endgroup$ – Jim Aug 28 '14 at 15:00
  • $\begingroup$ So what is this Velocity Edition Formula -Jim? $\endgroup$ – Harry David Aug 29 '14 at 10:09
  • $\begingroup$ @HarryDavid: see this question $\endgroup$ – John Rennie Sep 7 '14 at 5:33

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