Final answer:
The reaction time of the person who caught the meter stick is approximately 0.24 seconds, calculated using the second equation of motion with the given displacement (27 cm or 0.27 m), acceleration due to gravity (9.8 m/s²), and initial velocity (0 m/s).
Step-by-step explanation:
To calculate the person's reaction time who caught the meter stick, we will use the equations of motion under constant acceleration. Specifically, the second equation of motion which is s = ut + 0.5at², where 's' is the displacement of the meter stick, 'u' is the initial velocity (which in this case is 0, as the meter stick was released and not thrown), 'a' is the acceleration due to gravity, and 't' is the time, which in this case, is the reaction time we want to find.
Given:
s = 27 cm (or 0.27 m, since we need to work in SI units),
a = 9.8 m/s² (acceleration due to gravity),
and u = 0 m/s (initial velocity).
Substitute these values into the equation:
0.27 = 0 + 0.5 × 9.8 × t²,
0.27 = 4.9t².
Now, solve for 't':
t² = 0.27 / 4.9,
t² = 0.0551.
Therefore,
t = √0.0551,
t ≈ 0.235 s.
The reaction time of the person is therefore approximately 0.24 seconds.