A car is travelling in one direction at 80 km/h and a fly is coming from the opposite direction at 5km/h. (So its velocity is -5 km/h, since it's in the opposite direction.)
The fly hits the windshield of the car and is now travelling at 80km/h. In order for the fly to achieve the speed of 80km/h it's speed must have passed from -5km/h to 80km/h. (Meaning it must pass through the speed of zero) Therefore if the fly passes through a speed of 0km/h and the car is in contact with the fly the car must also pass through that speed of 0km/h.
This seems to mean that everytime a car gets hit by a fly it will completely stop. Why is this not so?
I believe there is another facet of this problem that is important in the real world solution. The analysis presented in the question assumes that both the fly and the car can be treated as "points". While for the majority of situations, this simplification greatly eases the nature of physics and Engineering problems, I believe that in this case an important quality of the collision gets left behind. The forces created by this collision arise out of the deformation of the objects (check out a picture or slow motion vidoe of a tennis ball that is in mid-bounce to illustrat my point) in question. Due to the huge difference in mass, the fly will "deform" much more than the car will. Also, with the car not represented as a single point, you can see that part of the car can deform, while the rest does not. Now with all of this in mind, my analysis of the situation is as follows. A very small piece of the car, while in midst collision, (may) experience zero (relative) velocity, the overall car does not experiance the slightest significant change in its velocity, while the fly undergoes a greatly significant velocity change.My next point is that there isn't a problem with a velocity of zero, as velocity is frame dependant. Re-consider the question from the reference frame of the police cruiser, travelling at 85 km/h to catch the reckless fly killing driver. Now the fly goes from 165 km/h to 5 km/h, so the car doesn't have to pass through zero at all...
not points
