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Re: [Phys-L] Falling - the tale of a simple 1st degree non-linear ODE

On 1/14/2019 4:03 AM, Richard Tarara wrote:
I trust David's solution is correct, but what about a really long fall where rho varies and maybe even long enough that g varies. This was the example I would use with my introductory (Calculus level) classes to show how using a simple spreadsheet could give reasonable solutions.  We dropped a bowling ball (my constant in-class prop) from the space shuttle at 100 km high.  /cut/

On the topic of long falls, it seems that a bowling ball dropped at Space Station altitudes (220 km) might well linger in the vicinity.
A Google executive named Eustace, recently hitched a lift in a helium balloon and detached at 41.18 km - exceeding mach 1 on the way down at times in  his 15 minute descent - a sonic bang heard at Earth's surface, apparently.
A NASA unmanned balloon prepared for an ascent lingered at 48 km for a time, recently.
Though g may only drop a few percent the atmospheric density drops much more dramatically at 100 km to perhaps  ~ 1 millibar.

Brian W