[Guest]

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?

[Guest]

ummm i don't think i understand the riddle cause it felt reallllly simple... the answer is 10kph?.. cause i mean why would the fly's velocity change? and where is the paradox?.. i'm conffuzzled.. oh and i'm wondering... does the fly get smushed at pt of contact or is it like above it?

^o^

[Guest]

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?

[Molly Mae]

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.

[Guest]

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?

[Molly Mae]

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.

[Molly Mae]

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.

[Guest]

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

[Guest]

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?

[Guest]

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

[Molly Mae]

I'm assuming that the paths of the fly and the train are collinear and each are traveling toward one another.

[Guest]

then if that is the case then and there is no turn as mentioned that yh the fact that it would get to a 0 is correct ... if not i blv the answer will change

[Guest]

what is up with me today! can't form a sentence without some form of slip up... i handed in an essay 2day...that should go nicely-_-'

[Guest]

look at it like this...

two cars are nearly going to crash. let's pretend that they didn't use the breaks or the there was ice and they couldn't stop.

If you were in one of these cars, and you looked and you checked the speed at the time of contact, the car wouldn't go any faster/slower until a fraction of a second later when the other car goes flying overhead.

Obviosly, 10km/h

[Guest]

i don't think the speed can be 10km at pt of contact.. when the cars hit the speed ofcourse goes down..and u also have to take into account that the fly is much smaller than the train.. the train will be un-effected by it crashing into it so it just keeps going

but the fly at pt of contact as to have decreased in speed or even reached zero... before going in the other direction

i liked a previous analogy of it by maurice.. imagine it as a baseball game..when the ball hits the bat it can't remain at the same speed as it was while flying when it hits the bat it has to decelerate and head in a different direction

and since in this case the fly and train are facing each other in a straight line then when the fly hits the train it will then start heading in the same direction as the train which is 180 it's original direction and for that to happen it must reach ,at a certain pt, tothe velocity 0

so i don't blv it to be at the same velocity at pt pf contact

if anything i think at pt of contact it is zero

Edited October 23, 2011 by guppy

[Molly Mae]

so i don't blv it to be at the same velocity at pt pf contact

if anything i think at pt of contact it is zero

Is the deceleration instantaneous? If not, why would the fly be slowing down before it hits the train? This is the core of the question. I believe the speed to be 0 a tiny fraction of a second after impact (which implies that the momentum of the fly affects the momentum of the train--which it does...but only so slightly).

[Guest]

ahahahah that's not really what i meant MM... i think i was trying to be polite by not being too blunt of whtvr... i was tired

we discussed this already and we got to 0 and i blv it to be 0 at contact.

.... mmm i see your pt... but is the train really effected .. even slightly?

the fly to the train might as well have been dust in the air to us while we walk...

dust doesn't effect us.... does it?0.0 i know either way it's negligible but does it even effect the momentum at all?

aren't some thing considered null? (although i do find logic in your reasoning and i do agree but i don't think it applies here or does it?)

Edited October 26, 2011 by guppy

[Molly Mae]

ahahahah that's not really what i meant MM... i think i was trying to be polite by not being too blunt of whtvr... i was tired

we discussed this already and we got to 0 and i blv it to be 0 at contact.

.... mmm i see your pt... but is the train really effected .. even slightly?

the fly to the train might as well have been dust in the air to us while we walk...

dust doesn't effect us.... does it?0.0 i know either way it's negligible but does it even effect the momentum at all?

aren't some thing considered null? (although i do find logic in your reasoning and i do agree but i don't think it applies here or does it?)

The fly's momentum (mass and velocity) certainly do affect the train, but not on any real measurable scale, so you could count it as negligible for the sake of any other problem, but does exist (since momentum can't be destroyed). The fact that the affect does exist, though, is proof enough that the fly decelerates to 0 after impact.

[Guest]

ahhhh well thank you MM that clears things up.. so basically what you are saying that there isn't usually a null factor but rather a negligible factor but the factor still exist no matter the speed or circumstance?

well i can make sense of it and it's logical so that's gd enough for me

so the fly reaches 0 at a tinnnnyy microsecond of time after impact with the train would be our final conclusion.

but using that logic u kinda feel weird when thinking that if u are walking and there is like bundles of dust particles in the air or if someone somehow throws droplets of water at you while walking or running, it effects your momentum. i would have never thought about it or assumed that they would

[voider]

People who have done high school physics will know that collisions are associated with a finite period of time. It is not inappropriate (for general purposes) to model the fly's acceleration as constant during contact.

The fly may end up sticking on the train, or bouncing off it. There are other complications with making use of the provided speeds.

Either way, the "moment" in question is not an instant, so if you took "moment" as "period of time" then the most informative answer might be:

v(t) = (v_f - v_i)/(Δt) * t + v_i, 0 <= t <= Δt

We know v_i = 10 kph.

[Guest]

The speed of the fly at the moment of contact is 10 kph.

The moment of contact is before deceleration has occurred due to the crumple of the fly.

There will be a moment when the speed of the fly is 0, before it begins to move with the train, assuming they are traveling on the same plane.