A roughly spherical meteor made mainly of iron (density about 8 grams per cubic centimeter) is hurtling downward through
the air at low altitude. At an instant when its speed is 1 × 104 m/s, calculate the approximate rate of change of the meteor's
speed. Do the analysis for two different meteors—one with a radius of 10 meters and one with a radius of 100 meters.
Start from fundamental principles. Do not try to use some existing formula that applies to a very different situation. Follow
the kind of reasoning used in this chapter, applied to the new situation, rather than trying to use the results of this chapter.
A major difference from our earlier analyses is that the meteor is traveling much faster than the average thermal speed of
the air molecules, so it is a good approximation to consider the air molecules below the meteor to be essentially at rest, and
to assume that no air molecules manage to catch up with the meteor and hit it from behind. The meteor drills a temporary
hole in the atmosphere, a vacuum, that gets filled explosively by air rushing in after the meteor has passed.
There is good evidence that a very large meteor, perhaps 10 kilometers in diameter, hit the Earth near the Yucatan Peninsula
in southern Mexico 65 million years ago and caused so much damage that the dinosaurs became extinct. See the excellent
account in T. rex and the Crater of Doom, by Walter Alvarez (Princeton University Press, 1997). Alvarez is the geologist
who made the first discoveries leading to our current understanding of this cataclysmic event.