Sunday, June 3, 2012

Ballparking: We Have a Winner!

Ladies and gentlemen, we have a winner!  To mix things up a bit, I decided to simulate this one.1  I used Mathematica for the simulation.  There is a gravitational force

F = m g

on the tennis ball.  Here, m = 57 g is the mass of the ball and g = 9.8 m/sis the acceleration due to gravity.  The wind can be represented by a drag force

F = C A ρ v2 / 2,

where C = 0.3 is the drag coefficient, A = 0.0036 m2 is the cross-sectional area of the ball, ρ = 1.2 kg/m3 is the density of air, and v is the velocity of the ball relative to the air.  I made an animation of the simulation below.

It turns out you need a wind of about 45 mph.  Congratulations to our winner!

[1] I know, I's supposed to be an estimation.  You know that scene in Raiders of the Lost Ark when Indiana Jones shoots the sword-wielding guy?  Well, it turns out that was supposed to be an elaborately choreographed fight scene, but Harrison Ford had severe diarrhea that day so he called an audible.  Spielberg loved it, so it stayed in the movie.  Why do I bring this up?  Do I have severe diarrhea?  No, but I was tired, lazy, and in the mood to simulate/animate something.  Plus, we had a lot of good estimates and I wanted to make sure my number was halfway decent.  Besides, I thought this one deserved a stick-figure animation.  Long story short, this was my "shooting the swordsman" moment.

Aaron Santos is a physicist and author of the books How Many Licks? Or How to Estimate Damn Near Anything and Ballparking: Practical Math for Impractical Sports Questions.   Follow him on Twitter at @aarontsantos.

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