Question

A meter stick is held vertically above your hand, with the lower end between your thumb and first finger. when you see the meter stick released, you grab it with those two fingers. you can calculate your reaction time from the distance the meter stick falls, read directly from 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 17.6 cm, what is your reaction time?

Answer 1

To calculate your reaction time based on the distance the meter stick falls, use the equation t = √(2d/g); substituting d = 17.6 cm, the calculated reaction time is approximately 0.19 seconds.

Step-by-step explanation:

To derive a relationship for your reaction time based on the distance the meter stick falls, we will use the kinematic equation for uniformly accelerated motion: d = ½ a t^2, where d is the distance fallen, a is the acceleration due to gravity (approximately 9.81 m/s^2), and t is the time taken to fall that distance. Solving for t, we get the equation t = √(2d/g), which allows us to calculate the reaction time.

(b) If the measured distance (d) is 17.6 cm (0.176 m), we substitute this value into the equation: t = √(2 × 0.176 m / 9.81 m/s^2), which gives us the reaction time. Performing the calculation, we find that t is approximately 0.19 seconds.