Question

Here's an interesting challenge you can give to a friend. Hold a $1 bill by the upper corner. Have a friend prepare to pinch the lower corner, putting their fingers near but not touching the bill. Tell them to try to catch the bill when you drop it simply by closing their fingers. It seems easy but it isn't. It would take them about 0.25 seconds to react and close their fingers— which isn't fast enough to catch the bill. How much time does it take for the bill to fall beyond her grasp? The length of the bill is 16cm.

Answer 1

The formula for falling in gravity from rest is

D = (1/2) (g) (t)²

Distance = (1/2) (gravity) (falling time)²

Solve this for time, and you find that

Time = √(2·distance/gravity)

For this problem, distance = 16 cm, and gravity on Earth always = 9.8 m/s².

Write those numbers in, and we get

Time = √(32 cm) / (9.8 m/s²)

time = √(0.32 / 9.8) (s²)

time = 0.18 second

The whole dollar bill falls through the catcher's fingers before he can pinch.  THAT's why a person can't react fast enough to catch the falling bill.