Step 1

In this case the bill is doing a free fall.

Let, the distance traveled be denoted by 's', the acceleration due to gravity be 'g' , time taken to fall be 't' , and the initial velocity be denoted by 'u'

Now, the given quantities:

\(s=16\) cm

\(u=0\) (as initially at rest)

\(g=9.8\ m/s^{2}\)

Apply the equation of motion to get,

\(s=ut+\left(\frac{1}{2}\right)gt^{2}\)

Step 2

put the values, to get

\(16\times10^{-2}=\frac{1}{2}\times9.8\times t^{2}\)

\(\Rightarrow t^{2}=\frac{2\times16\times10^{-2}}{9.8}\)

\(\Rightarrow t=0.18s\)

So, the time taken for the bill to fall beyond her grasp is 0.18s.

And as the average reaction time is 0.25s, so the friend would never catch it.

In this case the bill is doing a free fall.

Let, the distance traveled be denoted by 's', the acceleration due to gravity be 'g' , time taken to fall be 't' , and the initial velocity be denoted by 'u'

Now, the given quantities:

\(s=16\) cm

\(u=0\) (as initially at rest)

\(g=9.8\ m/s^{2}\)

Apply the equation of motion to get,

\(s=ut+\left(\frac{1}{2}\right)gt^{2}\)

Step 2

put the values, to get

\(16\times10^{-2}=\frac{1}{2}\times9.8\times t^{2}\)

\(\Rightarrow t^{2}=\frac{2\times16\times10^{-2}}{9.8}\)

\(\Rightarrow t=0.18s\)

So, the time taken for the bill to fall beyond her grasp is 0.18s.

And as the average reaction time is 0.25s, so the friend would never catch it.