## Baseball Physics

We went to a minor league baseball game on Sunday.

This photo provides an opportunity for a high school physics exercise. You can see the ball in the picture. It’s the blur on the right hand side.

**Problem** Begin by estimating the length of the blur. Then use this estimate to calculate the speed of the pitch. The exposure time for the photo was 1/80 of a second. First calculate the speed in feet per second. Then convert to miles per hour. (There are 5280 feet in a mile and 3600 seconds in an hour.)

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**Tags:** baseball, physics, pitch, speed

June 28, 2011 at 18:28

How fast is the baseball in the above image moving?

First, crop the image until only the relevant material is visible. Next, find the width and length of the blur, in pixels. The width is from (47, 7) to (51, 17) and the length is from (7, 19) to (86, 6), according to the highlighted dots on the attached image. Thus, the width is 2sqrt(29) pixels and the length is sqrt(6410) pixels. Since the circumference of a normal baseball is about 9 inches, its diameter is 9/pi inches. Proportionally, (9/pi)/2sqrt(29)=L/sqrt(6410). Solving for L gives about 21.2957 inches.

Image: http://img402.imageshack.us/img402/5466/img0350l.jpg

Since this image exposure is 1/80 seconds, the ball traveled L distance in that 1/80 seconds. For ease of comparison, this needs to be converted to miles per hour. The units inches/second can be converted to miles/hour by multiplying by (1 foot/ 12 inches) * (1 mile/ 5280 feet) * (60 seconds/ 1 minute) * (60 minutes/ 1 hour) or 5/88. So, 21.2957 inches/(1/80) seconds * 5/88 is about 96.7988 miles/hour. Due to the precision of the data, the most precise answer is 97 miles/hour.

Thomas Murphy

MSSM Student, Senior 2011-2012

July 12, 2011 at 23:23

Nicely written solution, Thomas!

September 22, 2011 at 21:48

97 isn’t bad for a minor league team! What team was it?

September 24, 2011 at 19:22

The Fishercats (Manchester, NH).