Chapter 4, Problem 59A

You can compare your reaction time with that of a friend by catching a ruler that is dropped between your fingers. Let your friend hold the ruler as shown in the figure.

Snap your fingers together as soon as you see the ruler released. On what does the number of centimeters that pass through your fingers depend? You can calculate your reaction time in seconds by solving $d=\frac{1}{2}g{t}^2$ for time: $t=\sqrt{2d/g}$. If you express d in meters (likely a fraction of a meter), then $t=0.45\sqrt{d}$; if you express d in centimeters, then $t=0.45\sqrt{d}$. Compare your reaction time with those of your classmates.

To determine

The factors on which the number of centimeters that will pass through a person fingers depend.

To find: The reaction time of a person.

To compare: The reaction time of a person and his time.

Answer to Problem 59A

The numbers of centimeter pass through fingers directly depends on person average reaction time.

Person average reaction time is $0.127$ seconds.

The reaction time of the friend is 0.142 seconds.

Explanation of Solution

Given:

The given figure is shown below.

Formula used:

Reaction time is given by the following formula;

  $t=0.045\sqrt{d}$

Calculation:

Assume that, a person snap fingers at 8 cm on ruler and his friend snap fingers at 10 cm on ruler

So, for person $d=8$ cm and for his friend, $d=10$ cm An average reaction time of a person is,

  $t=0.045\sqrt{8}$

  $t=0.127$ seconds

The friend’s average reaction time is,

  $t=0.045\sqrt{10}$

  $t=0.142$ Seconds

It is observed that reaction time of a person is less than the friend’s reaction time. If reaction time is more than centimetres, it will snip between the fingers. Thus, it can be concluded that the numbers of centimeters that will pass through fingers depends onaverage reaction time.