# How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.

Here's an interesting challenge you can give to a friend. Hold a \$1 (or larger!) bill by an upper corner. Have a friend prepare to pinch a lower corner, putting her fingers near but not touching the bill. Tell her to try to catch the bill when you drop it by simply closing her fingers. This seems like it should be easy, but it's not. After she sees that you have released the bill, it will take her about 0.25 s to react and close her fingers - which is not fast enough to catch the bill.

How much time does it take for the bill to fall beyond her grasp? The length of a bill is 16 cm.

The time taken by the bill to travel throught the fingers is, s=\frac{1}{2} g t^{2}

Here, g is acceleration due to gravity, t is time and s is length of the bill.

t=\sqrt{\frac{2 s}{g}}

=\sqrt{\frac{2(0.16 \mathrm{~m})}{9.8 \mathrm{~m} / \mathrm{s}^{2}}}

=0.18 \mathrm{~s}

Which is lessthan the reaction time (0.25 \mathrm{~s}) of the person. So, she cannot catch the bill. Therefore, the time taken by the bill to fall beyond her grasp is 0.18 \mathrm{~s}.

### Raymond Puzio

Raymond Puzio has a PhD in Physics from Yale University. I have been creating PlanetPhysics with Aaron Krowne and Ben Loftin since 2005.