In a cognitive science study evaluating a pilot's reflexes under simulated G-force conditions, a vertical test apparatus is used. A heavy physical indicator is suspended electromagnetically. When the electromagnet is deactivated, the indicator falls freely from rest. The pilot must depress a control switch as quickly as possible the moment they see the indicator begin to descend. The vertical distance, yyy, that the indicator falls before the switch is successfully depressed is recorded.
Using equations of motion, derive an expression for the reaction time TTT of the pilot in terms of the vertical distance yyy and the acceleration due to gravity ggg. State any assumption made regarding external forces acting on the indicator during its fall.
In one calibration trial, the indicator falls a distance of 44.1 cm44.1\text{ cm}44.1 cm before the control switch is depressed. Calculate the pilot's reaction time, using g=9.8 m/s2g = 9.8\text{ m/s}^2g=9.8 m/s2.
Explain why it is crucial that the electromagnet is deactivated at irregular, unpredictable times during repeated trials, rather than at regular intervals.