Here's a really interesting mathematical explanation on how the "catch a dollar" trick works. You know the trick: a person holds a bill vertically and says you can keep the bill if you can catch the dollar with your fingers when it drops. You never catch it. It's really hard! Why?
As Numberphile explains, the reaction time in most humans is about 0.2 seconds. That is, it takes about that much time for our eyes to tell our brains to tell our body to do something (in this case, catch the bill). That doesn't seem that long though, so why is still so hard to get the dollar?
It can be explained with the free fall formula for distance (1/2 gravity x the square of the time falling). When you fill in the formula (gravity at 9.8 m/s and our 0.2 reaction time), you'll find what is basically, sort of the human reaction time in physical form: 20 cm. In order to catch something, you'll need it to travel more than 20 cm. A dollar bill measures less than 20 cm (around 15 cm), so you can't react in time before the dollar bill falls all the way through.
Obviously, some people have faster reaction times, so this doesn't apply to everybody — but who knew maths could be so delightful?