if a fly is flying in the opposite direction to a train speeding at 100 mph..the fly must change direction from oving forwards to moving backwards with the train...therefore there must be a point between the fly changing direction in which the fly has stopped moving. If the fly has stopped then so has the train.
Firstly, the fly only ever stops moving if it would go from forward motion straight to backward motion (reverse). Flies don't do this, they just turn real quick. Secondly, IF the fly stopped moving why would the train stop moving as well ? There is no real connection between the train and the fly, in other words.. its pure nonsense.
Two things here. First, for this puzzle to work you would have to assume that the train was a perfectly rigid body. In real life, the very front of the train (probably no more than the outer surface of the paint) would deform slightly as the fly impacted. It would be rather like gluing a pillow to the front of a car and whacking it with a bat as it drove by. The car never stops moving forward, but the surface of the pillow itself does stop (or even move backward slightly) because it's a compressible material. Similarly, when the fly hit the train there would be a microscopically small outer-layer of the train that compressed itself as the fly impacted, because the outer-layer would have been stopped by the fly even though the train was still moving. Second, even if you had some hypothetical train that was perfectly rigid and the fly collided with it perfectly elastically, there would be no need for the train to stop just because the fly has stopped, because in your scenario the fly is only stopped for an infinitely small period of time - the exact, infinitely small moment in which the collision occurs. Since we would also expect the distance traveled by the train to be zero over an infinitely small period of time regardless of its velocity, there is no paradox
Hm ok, I understand know that you let the fly hit the train. I didn't figure that from the OP. I believe Nasor answered your question perfectly already, no need to repeat Please Register or Log in to view the hidden image!
Apologies, i didn't understand the question the first time. Please Register or Log in to view the hidden image!
Please Register or Log in to view the hidden image! I'm not sure that you understand the hypothetical question any more than, Enmos...if the fly deviates from going forward to going backwards then between that nanosecond the fly is inbetween fwds/bwds. Got that. Now if the fly in the nanosecond the fly is not going fwds or back therefore it must by definition be inbetween..like a Car if a car crashes into another it may be going backwards but it has to crash to go backwards. It does not matter that one car is going faster because at the point of impact both are - for a moment - stopped in motion not just the fly (or the slow car) but the train (the fast car).
Not really, Enmos..but one at least admires your consistency in getting everything wrong by any means possible.
No offense, but I don't think you understand how collisions between perfectly rigid bodies work. There is only one specific, infinitely short instance of time in which the fly is "changing direction". You seem to be imagining that the fly is stopping for a very small but non-zero amount of time when it hits the train, as shown by your description of the time that the fly is stopped as being a "nanosecond." That's not the case. Even a nanosecond is a non-zero duration of time, and if the fly was actually stopped for a nanosecond then there would indeed be a logic problem here. But that's not the case.
The fly cannot suddenly go from a forwards motion to a backwards motion without anything inbetween. Its a very simple point.
The classic case as given to me 30 years ago was a ball-bearing rather than a fly. It does stop, while in contact with the train. The train also, therefore, stops. The flaw in the thinking is the use of the word "train". PART of the train stops - the part in contact with the fly/ ball bearing - that's why there's a dent in the front of the train afterwards (although admittedly in the case of the fly a very small dent Please Register or Log in to view the hidden image!). The impact causes deformation in the material of the train (the part which actually stops), this deformation allows the rebound of the ball bearing as it passes through zero velocity and reverses direction. "The train" is not a monolithic structure... easy.
Sure it can. Have you ever had a physics class? Suppose the fly and the train are 2 meters apart, and are each moving forward toward each other at 1 m/sec. Before time=1 second, they will each be moving toward each other. At exactly time=1 second, they collide. Immediately after t=1 sec, the fly and the train are both moving in the same direction. The only time the fly is stopped is at exactly t=1 sec. If you are any time before or after t=1, the fly is not stopped; it either moving forward or backward. The instant of t=1 is a point in time, not a duration of time.
Pieces of the fly (like a squishy accordian) will achive zero velocity for a few billions of a billionth of a second; however, those same pieces will have 100 mph acceleration.
