Reaction Time: Softball, Baseball

Date: 04/26/2003 at 06:12:55
From: Sam
Subject: Softball pitchers vs baseball pitchers

Dr. Math,

The other night at our high school we had girls' softball and boys' 
baseball games going on at the same time. The baseball pitcher was 
throwing 90mph from 60 feet, and the softball pitcher was throwing 
60mph from 40 ft. I argued that the reaction time for batters in 
softball was less than for hitters in baseball despite the difference 
in speed.

How can I measure reaction time for each? (60 mph from 40 ft vs 90mph 
from 60 ft)

If my assumption is correct that the reaction time is less in softball 
for hitters, then how fast would a baseball pitchers' pitch have to be 
to equal the reaction time for a softball player (from 60 ft).

Thank you,
Sam Henderson

Date: 04/26/2003 at 09:48:48
From: Doctor Paul
Subject: Re: Softball pitchers vs baseball pitchers

The batter's reaction time is equal to the amount of time it takes for 
the ball to travel to the plate from the moment it is released from 
the hand of the pitcher.

In the softball case, the ball is traveling 60 mph for 40 feet.  How 
long does that take?

60 miles      1 hour      1 minute    5280 feet    88 feet
-------- *  ---------- * ---------- * --------- =  --------
1 hour      60 minutes   60 seconds    1 mile      1 second

Thus 60 mph = 88 feet per second.

If the softball is moving at 88 feet per second, how long will it 
take to go forty feet?

We want to solve for x:

88 feet     40 feet
-------- =  --------
1 second    x seconds

88*x = 40 

x = 40/88 = .454545454545... seconds

So the reaction time for the softball hitters is .45 seconds.

Similar calculations show that

90 mph = 132 feet per second

We want to solve:

132 feet   60 feet
-------- = -------
1 second   x seconds

x = 60/132 = .4545454545... seconds

So the reaction time is exactly the same and that answers your second 
question.

I hope this helps. Please write back if you'd like to talk about this 
some more.

- Doctor Paul, The Math Forum
  http://mathforum.org/dr.math/