Question

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.

Answer 1

Answer:

t <t _reaction

We see from this that the bill passes completely through the fingers before the reaction time (time without movement) passes and therefore before closing the fingers.

Explanation:

In this exercise we can use the free fall kinematics, let's calculate the time that the upper corner of the bill takes to pass through the fingers of her friend, when releasing the bill it starts with zero speed, let's use the equation

         y = v₀ t + ½ g t²

         y = ½ g t²

         t = √(2y / g)

let's calculate

         t = √ (2 0.16 / 9.8)

         t = 0.18 s

the reaction time is

         t_reaction = 0.25 s

Thus

         t <t _reaction

We see from this that the bill passes completely through the fingers before the reaction time (time without movement) passes and therefore before closing the fingers.