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Speed of a fly inside a car

Just a conceptual question: If a flying bee is inside a speeding vehicle, will it have to "fly" just as fast as the vehicle to stay aloft inside the car during the journey? It logically seems true but any thoughts?

For the sake of simplicity, let us assume that the windows are closed and no air can get in or go out (i.e. isochoric), let us also assume that the bee can only travel along a straight line (thus no random movements). Will the bee slam against the walls if it fails to comply with the speed of the car? Will the bee experience this and actively start flying ahead faster?

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Consider that this is the same as suggesting that you would have to run at the same speed as the car to avoid being smashed by your seat. –  Colin K Apr 15 '12 at 12:50
First two questions are unrelated - no acceleration. Only the helicopter case is related. –  Pygmalion Apr 15 '12 at 13:17
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marked as duplicate by Qmechanic, Manishearth, dmckee Apr 15 '12 at 13:05


1 Answer

I think it would be fair to assume, that all of the air within the car will go as fast as the car does. So, air drag will actually accelerate bee in the direction of the car's acceleration. Since air drag is rather small, bee's acceleration $a'$ would be much smaller than the acceleration of the car $a$ and bee would eventually hit the last part of the car. The approximate relative speed with which bee hits the car is $v^2 = 2 (a-a') s$, where $s$ is typical dimension of the car. (Why approximate? $a'$ isn't constant, it depends as relative velocity of bee within air squared $v_\text{r}^2$. The exact expression would require solving differential equation.)

It is hard to speculate about bee's reaction, but my guess would be that bee would tend to fly against air drag, therefore annuling $a'$.

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