Question

How to do this?

1. A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. On seeing the meter stick released, you grab it with these two fingers. Your reaction time can be calculated from the distance the meter stick falls, read directly from the scale at the point where your fingers grabbed it.
   a) Derive a relationship for your reaction time in terms of this measured distance, d.
   b) If the measured distance is 18.6 cm, what is the reaction time?

Answer 1

a) the relationship between your reaction time and the distance d in cm is `t=sqrt(2/g d/100) = 0.045 sqrt d`.
b) If d=18.6 cm, the reaction time `t= 0.045 sqrt 18.6 = 0.19` in sec.

Explanation:

a) Remember that the axcelleration of gravity, `g= 9.81` m/s².

When an object starts at standstill, it will, therefore, have dropped a distance `s= 1/2 g t^2` after t seconds, where s is the distance in m. For our purposes it is easier to work with the distance `d=100s` in cm.

Now we can read the distance d on the meter stick, and the time t, therefore, will be
`t= sqrt(2/g s) = sqrt (2/9.81 d/100)= 0.045 sqrt d`.

b) If the measured distance is d=18.6 cm, the reaction time t will be
`t= 0.045 sqrt 18.6 = 0.19` to the nearest 1/100 second.