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### #1 GuinnessPax

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Posted 27 September 2011 - 09:25 PM

A recent brain teaser made me remember this paradox:

If a train is travelling at 100kph. A fly is flying directly towards it at a speed of 10kph.

What is the speed of the fly at the moment of contact?
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### #2 guppy

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Posted 28 September 2011 - 05:32 PM

Spoiler for feeling dumb...:S

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### #3 maurice

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Posted 28 September 2011 - 07:23 PM

Think of it this way, guppy.

Right before impact, a fraction of a second before, it is traveling 10 k/h. A fraction of a second later it is essentially moving in the opposite direction @ 100 k/h. There was never anything in between, as say would happen if you hit the brakes and slammed on the gas in reverse. So what speed is the fly traveling at at that exact instant in between?
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### #4 Molly Mae

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Posted 28 September 2011 - 07:49 PM

Plot it and you'll find the speed change as the time changes, I'm sure. It just takes billionths of a second to decelerate to 0 and then accelerate in the opposite direction.

Ah, but I think I'm starting to see the paradox. If the point of impact is 0, why is the fly decelerating before impact?

Regardless, I believe that there would be a point where the fly is traveling at 0 km/h in the same manner that a ball thrown straight up into the air will eventually stop and begin to accelerate back toward earth. Sure the acceleration of gravity isn't initially as forceful as a train pushing a fly in the opposite direction, but it's still an outside force.
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### #5 maurice

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Posted 28 September 2011 - 07:59 PM

Yeah, MoMa, Imma see this like a batted ball. The ball doesn't decelarate (due to the bat at least) until impact. But the deceleration occurs while the energy is being transferred (or smith like that). So at impact, which due to some sort of absorption prolly isn't a moment, the speed is 0 k/h as expected...right?
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### #6 Molly Mae

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Posted 28 September 2011 - 10:59 PM

Yeah, MoMa, Imma see this like a batted ball. The ball doesn't decelarate (due to the bat at least) until impact. But the deceleration occurs while the energy is being transferred (or smith like that). So at impact, which due to some sort of absorption prolly isn't a moment, the speed is 0 k/h as expected...right?

Well, let's look at it another way. Imagine a t-ball is resting and waiting to be hit from the tee. You swing the bat and there is a one-way* energy transfer (the ball has 0 momentum at rest) that gives the ball momentum.

Now we throw a ball at a brick wall. When it hits, the ball loses momentum* and falls to the ground.

Now, let's combine the two. The ball is at 0 k/h only before the bat makes contact, but only after it hits the wall. Is there any time between these two events? In the fly + train problem, there isn't. They're the same event. The only conclusion, then, is that if there is ever a time when the ball/fly is at 0 k/h, it must be at the exact moment of impact.

*Per Newton's Third Law of Motion, this isn't true, but we're not really concerned with the extra details.
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### #7 Molly Mae

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Posted 29 September 2011 - 03:05 PM

On my drive home, I actually thought further about this and realised that there's a flaw in my logic above.

But now I can't seem to get this problem out of my head. There must be more than an instant where the fly decelerates. Like Newton's Cradle.

But this also assumes that the fly and train are traveling directly toward each other and that the fly's direction of travel changes by exactly 180 degrees. Otherwise, I will argue that the fly will never be at 0 k/h.
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### #8 guppy

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Posted 29 September 2011 - 03:14 PM

mmm thank you maurice for taking the time to explain it i get it now....
and i also came with the same conclusions.. it is a veryyyyy small fraction in time but it definitely exists... i merely imagined it in slow motion
for anything to change in a opposite direction it has to lose the build up it had before and then gain the new build of velocity
now u see this was solid in my head just a few seconds ago and i was fully convinced when i was thinking it... but now i don't know why.. i feel there is something amiss
imean it's not like the fly hit the wall and the wall theeen started moving... i mean consider yourself running very fast you can change direction without losing momentum or atleast not all momentum...
the train is faster than the fly so i'm wonder if the fly ever did lose momentum if there was an actual time when it hit zero.... but maybe i guess cause the fly is heading in a 180 degree twist after pt of contact it does but i'm not sure... it depends what happened with the direction of the fly after contact with the train
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### #9 guppy

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Posted 29 September 2011 - 03:24 PM

ahahhahahahaha molly mae your post came up minutes before mine and i just saw it
yes i totally agree ... the theories we lead before are circumstantial... it has to be a 180 twist for it to apply
i'm wondering now of the direction of the train at the exact moment and after contact with the fly and how it could work to not be 0 ... i think i got something
imagine if the train were at the exact moment of the fly hitting it took a turn or something.,. would the flies velocity actually get to zero ?
and when i first read the riddle i imagined them opposite to each other but now i'm think ... the fly could be coming at it from the side ... and still be going directly towards it right?
i mean u don't have to be facing the front end of something to be going "directly towards" it right?
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### #10 guppy

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Posted 29 September 2011 - 03:25 PM

excuse my grammar mistakes... i reread it now and noticed some
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