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Originally Posted by grav
Okay, let's say two observers are moving toward each other with a relative speed of 30 m/sec. (snip)...
...Now, to the catcher, the ball was thrown when it was 20 meters away and travels that entire distance to her.
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No it doesn't. It doesn't travel the entire distance for,
while the ball is in flight, Catcher C is closing the distance to Thrower T.
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She will see the thrower lag behind the ball, but it does not matter how the thrower travels after the ball is thrown. So to the catcher, the ball has travelled 20 meters at 40 m/sec, so takes 1/2 second to reach her.
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No it hasn't. The original distance the ball had to travel might have been 20m, but that's not how far the ball went. It went some distance
less than 20m.
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From the perspective of the thrower, however, the ball was only thrown at 10 m/sec relative to him, but the catcher is also moving toward him at 30 m/sec.
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The ball is travelling at 40m/sec.
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So during the time the ball is in flight,
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Less than 1/2 sec.
Less than 20 meters... Maybe 15.5m.
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...1/4 of the distance toward the catcher
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...3/4 of the original (at time of throwing) distance to C.
[/quote]while the catcher travels the other 3/4 of the distance toward the ball. [/quote]while C travels the 4.5m towards the ball.
This must be T.
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...the catcher has travelled 15 meters of the original 20 meters
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...C has travelled 4.5m. of the original (Time of throwing) 20 meters.
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...while the ball has only travelled 5 meters.
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The ball has travelled 15.5m.
T?
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...sees the ball travelling 5 meters at 10 m/sec,
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...sees the ball travelling 15.5m at 40m/sec.
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...the time of travel is 1/2 second...
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...the time of travel is less than 1/2 sec.
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... the same as that for the catcher, but the distance travelled is quite different.
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...The same as that for C? But the distance travelled (by the ball? By T? By C?) is quite different...?
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The question is, if all of these speeds are relative between observer and each observer and the ball, so that either can consider themself stationary and measure the same duration of flight of the ball, but over different distances travelled, then which one is right? What is the true distance the ball has travelled, 5 meters, 20 meters, or something else?
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15.5m. I don't have any difficulty with that, at all.