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No Time to Stop and Think

The baseball season is back, and with it, some great mathematical opportunities...

Known Fact: Randy Johnson, future Hall of Fame pitcher, and his fast ball easily could average 90 mph on a hot afternoon.

Question 1: Given that the distance from the pitcher's rubber to home plate is 64 feet, how much time does a batter have to react to Randy Johnson's 90 mph fast ball?

Question 2: How much less time does a batter have to react if Randy Johnson uses a 100 mph fast ball? Or, more time for a 85 mph change up?

 


Hint: If your answer is more than "one second," try again...

 


Solution Commentary: Consider this interesting commentary by writer Davin Colburn and Ryan Zimmerman, who plays for the Washington Nationals: "A 90-mph fastball can reach home plate in 400 milliseconds ó or four-tenths of a second. But a batter has just a quarter-second to identify the pitch, decide whether to swing, and start the process. 'Once the pitch is in flight, itís the snap of your fingers,' Zimmer-man says. What happens next is 'pretty much just instinct.' A batter takes 100 milliseconds to see the 3-in. ball, and 75 milliseconds to identify spin, speed and pitch location. The batter has another 50 milliseconds to decide whether to swing, and where, before he must act. It can take nearly 25 milliseconds for the brainís signals to pulse through the hitterís body and start his legs moving. The swing itself takes 150 milliseconds."