Precision during free-fall experiments.

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I'm not sure how to answer this question, so I'm turning to you guys for help.

The question, specifically, is: "When timing the fall of a ball, how would you achieve greater precision, with larger or smaller heights?"

Any help would you appreciated.
 
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Mathematically, in larger heights. It's all about relative error (which is the mathematical expression for precision). Imagine you have a timer that measures until 0.01 seconds then the greater the time you get is the smaller the % of it it will be 0.01.

Just tell if you don't see it ;)