Question

You are doing an experiment to determine your reaction time. Your friend holds a ruler. You place your fingers near the sides of the lower part of the ruler without touching it. The friend drops the ruler without warning you. You catch the ruler after it falls 11.3 cm . What was your reaction time? please show formulas and explanation step by step

Answer 1

I'm guessing that you mean like this:
-- The ruler is held with zero at the bottom, and the centimeter markings
    increase as you go up the ruler.
-- You place your fingers with the ruler and the zero mark between them.
-- The number where you catch the ruler is the distance it has fallen.

Then, all we have to find is the time it takes for the ruler to fall 11.3 cm .

Here's the formula for the distance an object falls from rest
in a certain time:

                Distance = (1/2) (gravity) (time)²

On Earth, the acceleration of gravity is 9.8 m/s².
So we can write ...

                              11.2 cm  =  (1/2) (9.8 m/s²) (time)²
or
                         0.112 meter  =  (4.9 m/s²) (time)²                      

Divide each side
by  4.9 m/s² :        (0.112 m) / (4.9 m/s²)  =  time²

                            (0.112 / 4.9)  sec²  =  time²

Square root
each side:            time = √(0.112/4.9  sec²)

                                  =  √ 0.5488 sec²

                                  =      0.74 second     (rounded)  

Answer 2

Answer:

0.152 seconds

Explanation:

Distance travelled by the ruler = 11.3 cm = s

Initial velocity of the ruler = 0 = u

Final velocity of the ruler = v

Time taken by you to catch the ruler = t

a = Acceleration due to gravity = 9.81 m/s²

Equation of motion

$s=ut+\frac{1}{2}at^2\\\Rightarrow 0.113=0t+\frac{1}{2}9.81t^2\\\Rightarrow t^2=\frac{2\times 0.113}{9.81}\\\Rightarrow t=\sqrt{\frac{2\times 0.113}{9.81}}\\\Rightarrow t=0.152\ s$

So, it took you 0.152 seconds to react to the ruler falling.