Question

Rob challenges Abe to catch a dollar bill in this way: She holds the bill vertically, with the center of the bill between Dave's index finger and thumb. David must catch the bill without moving his hand. If his reaction time is 0.2s, will he be able to do it? Explain. *The dollar bill is 15.5 cm long

Answer 1

Just to make it all a bit easier...
\[\Large \begin{array}{l}
15.5{\rm{cm}} = 0.155{\rm{m}}\\
\frac{{0.155}}{2} = 0.0775{\rm{m}}
\end{array}\]
So the bill is being held at about 0.0775m from the end. The acceleration due to gravity is \(9.81{\rm{m}}{{\rm{s}}^{ - 2}}\), and using the equation \(s = ut + \frac{1}{2}a{t^2}\) we can work out how long it will take the bill to travel that far; the bill's starting from standstill, so...\[\Large \begin{array}{l}
s = ut + \frac{1}{2}a{t^2}\\
u = 0\\
{t^2} = \frac{{2s}}{a}\\
t = \sqrt {\frac{{2s}}{a}} \\
= \sqrt {\frac{{2 \cdot 0.0775}}{{9.81}}} \\
= 0.126{\rm{s}}
\end{array}\]
So no, the bill would not be caught if the normal reaction time is 0.2s.