In a reaction-time experiment, a student holds a ruler vertically. A classmate places their open fingers level with the zero mark of the ruler, ready to catch it. Without warning, the student drops the ruler, and the classmate catches it as quickly as possible. The distance ddd that the ruler falls before being caught is measured.
Using equations of motion, derive the expression for the reaction time ttt of the classmate in terms of the distance ddd and the acceleration due to gravity ggg. Assume air resistance is negligible.
In one trial, the ruler falls a distance of 19.6 cm19.6\text{ cm}19.6 cm before it is caught. Calculate the classmate's reaction time, using g=9.80 m/s2g = 9.80\text{ m/s}^2g=9.80 m/s2.
Explain why it is important for the student to release the ruler at random times during repeated trials, rather than at regular intervals.