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If reaction time is genuinely a source of error in such experiments
then you need to go back to the drawing board and redesign the
experiment. Reaction time can only affect such measurements if, for
instance, a) you let your partner drop the ball while you run the
stopwatch AND you insist that your partner give you no warning or b)
you consciously refuse to watch the ball as it drops and wait for the
sound of the ball hitting the floor before stopping the watch.
Of course there will be variations in the times obtained from
successive time trials, but I maintain that they have essentially
nothing to do with the phenomenon that is properly called "reaction
time."