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FW: baseball pitching speeds
Posted:
Aug 9, 2000 10:24 PM


 From: Michael Paul Goldenberg <mikegold@umich.edu> Date: Wed, 09 Aug 2000 21:36:16 0400 To: keckcalc <keckcalc@earthlink.net> Subject: Re: baseball pitching speeds
If the fastest professional pitchers throw at around 100 mph using the force of their legs driving them and the leverage gotten from the mound, it seems doubtful that ANYONE could throw a baseball at 100 mph vertically. That's just my very strong intuition.
> From: keckcalc <keckcalc@earthlink.net> > Date: Wed, 09 Aug 2000 17:45:15 0800 > To: Terry Trotter <terry@mathforum.com>, mathteach@forum.swarthmore.edu > Subject: Re: baseball pitching speeds > > > > Terry Trotter wrote: > >> I need a little help with a number. Being that I'm weak in physics, I >> would like someone to give me a reasonable approximation about how >> fast a top star professional baseball pitcher could throw a baseball >> vertically into the air. (Not horizontally to a batter; there could >> be a difference, or perhaps some similarity.) I'm desiring a number >> expressed in feet per second or meters per second. >> I need this to compose a future problem for the Math Forum's >> Problem of the Week project. Thanking you for your kind assistance. > > Hi, Terrel, > > An interesting question with which I have delt indirectly. In a course I > have taught called Geometry and Algebra with Transformations the > introduction to parabolas is motivated by seeking to describe the pattern > in data collected as a basketball is tossed over a motion sensor. This > little event takes place in the classroom, but once certain mathematical > ideas are formed, I have taken students to the school athletic field > where we set up one of the school's pitching machines so that it will > project baseballs or softballs as close to straight up as we can manage. > (There have been times when a ball launched at 50 miles or more per hour > has landed only a few feet from the launcher (me) who feeds the machine.) > > When the launching takes place, I think the only realistic measurements > we can make are of the duration of the flight and the distance from the > ground to the last point of contact between the ball and the pitching > machine. When we "borrow" the approximately negative 16 quadratic > coefficient arrived at through an analysis of the basketball toss data, > we are able to use the two additional measurements to complete the > description of a parabola which we have reason to expect would model > (time in seconds since the launch, position of the ball relative to the > launch point) data. We get an impression of the reasonableness of such > quadratic models by using them to compute the average velocity over the > first thousandth of a second and comparing that computed value to the > settings on the pitching machine. > > It takes a very high initial velocity to get the ball in the air for > about seven seconds. I remember reading somewhere that the record time > for a thrown baseball in the air was a little over eight seconds. Thus, > if on this record toss the ball had been thrown straight up, the velocity > would have been over 100 miles per hour. This is as fast as I have ever > heard for a thrown baseball. > > Good luck with your problem creation. Students do find the experiments I > describe above one of the highlights of the course. > > Sincerely, > > Richard Sisley > > > > > >> >> >> Terrel Trotter >> AlgPoW Coordinator



