Q41E - University Physics with Modern Physics

Question

A Simple Reaction-Time Test. 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?

Step-by-Step Solution

Answer

(a) Relationship between rection time and measured distance is  $t=\sqrt{\frac{2d}{g}}$.

(b) Your reaction time is  $t=0.189 \text{s}$

Step 1: Given data

Considered a meter stick it stands up, and its initial vertically velocity  $v_y=0 m/s$

Its acceleration is equal to the acceleration due to gravity (g).

Measured distance is  $17.6 \text{cm}\left(\frac{1 \text{m}}{100 \text{cm}}\right)=0.176 \text{m}$

Step 2: (a) Derive the relationship

For upward motion is considered negative and for downward motion,it is considered positive.

According to Newton’s second law of motion, the distance can be expressed as, 

$d=v_{y}t+\frac{1}{2}g{t}^2\cdots \left(1\right)$

Substituting the given values we get,

$t=\sqrt{\frac{2d}{g}}\cdots \left(2\right)$

 Step 2: (b) The reaction time

 

Since the measured distance is $d=0.176 \text{m}$ , then time can be calculated using the equation (2),

 $$\begin{gathered} t=\sqrt{\frac{2\times \left(0.176m\right)}{\left(9.8m/s^2\right)}} \\ =0.189s \end{gathered}$$

Thus, your reaction time is  $t=0.189 \text{s}$