[OT] Simple math considered physics; turns out it's fun, not harmful

[mike miller]

The real physics (1960's vintage, no calculators, no linux) answers (plural) 
are even simpler.  If you're asking how fast is the ball going, it's going 
50mph.  If you're asking how fast does it appear to be going based on time 
of flight from the pitchers mound to the batter, the answer is 100mph. 
60.5' is about double the actual 33' over which the ball is being pitched in 
the batting facility.  If the ball is to cover twice the distance in the 
same time, it must be going twice as fast.  I agree that my estimate of 
doubling distance is about 10% off so the ball would actually only appear to 
be going about 90mph.  That's still not accurate to 4 significant figures, 
but we're looking for the physics solution, not the engineering solution 
(you've heard the one about the physicist, engineer and mathematician whose 
houses caught fire) and I doubt most batters could tell the difference 
between a 90mph and a 91.66mph pitch.

Mike Miller
----- Original Message ----- 
From: "Greg Rundlett" <greg.rundlett at gmail.com>
To: "GNHLUG" <gnhlug-discuss at mail.gnhlug.org>
Cc: "Geoff Rundlett" <geoff at rundlett.com>
Sent: Wednesday, November 21, 2007 5:51 PM
Subject: [OT] Simple math considered physics; turns out it's fun, not 
harmful


>I really like the indoor batting facility in Salisbury, MA (Extra
> Innings).  I wondered how 'fast' the fast cage was.  It seemed really
> fast and has taken me a few visits to get to the point where I can hit
> the ball.  I asked today how fast the machine was.  The friendly staff
> person told me it pitches at 50mph and the machine is 33ft. from the
> plate.  A regular pitcher's mound is 60.5 ft from the plate.  He said
> if I have some friends who know physics I could figure out how fast
> that is in the big leagues.  I'm not making fun of the guy, but
> physics isn't involved in solving the problem, just regular math.
>
> nb: there are 5,280 feet / mile
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> spoiler: the answer is below.  If you want to figure it out for
> yourself, stop here for a bit.
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> 'fast' batting cage speed
> 50 miles / 1 hour = 264,000 feet / 3,600 seconds  = 73.333 feet / second
> X = elapsed time to home plate =
> X seconds / 33 feet = 1 second / 73.333 feet
> 73.333X = 33
> X = .45 seconds
>
> Y = Big League pitch speed =
> 60.5 feet / .45 seconds = Y feet / 1 second
> Y = 134.444 feet / second * 3600 / 5280 = 91.66 mph
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>
> That's fast.  It's also faster than the guy said.  He said it was
> supposed to be somewhere in the 70 mph range.
> Perhaps the numbers are off.  There is another 'VERY fast' cage that
> supposedly throws 60mph and is slightly further away (like 33.5 feet).
>
> I don't know whether I should be happy (I am) that I can hit the
> equivalent of a 91mph fastball.  Or, if I should be sad that an
> average person might think that there is physics rather than math
> involved.
>
> -- 
> A: Yes.
>> Q: Are you sure?
>>> A: Because it reverses the logical flow of conversation.
>>>> Q: Why is top posting annoying in email?
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