4. analysis\na. reaction time\nto begin with, we must relate a dropped distance to a time to fall that…

4. analysis\na. reaction time\nto begin with, we must relate a dropped distance to a time to fall that distance. using your knowledge of kinematics and free - fall motion, determine the time to fall a distance y. find this symbolically. show your work below. you should arrive at t = (\\frac{2y}{g})^{1/2}\nyou will determine the reaction time for each fall and record it in table 1. next, you will calculate the average reaction time and standard deviation for each data set, visual and audible\ntable 1. visual and audible reaction distances and related times\n|trial #|visual trials (m)|visual reaction time (s)|audible trials (m)|audible reaction time (s)|\n|----|----|----|----|----|\n|1| | | | |\n|2| | | | |\n|3| | | | |\n|4| | | | |\n|5| | | | |\n|6| | | | |\n|7| | | | |\n|8| | | | |\n|9| | | | |\n|10| | | | |\navg visual reaction time _____________, and std dev ____________________\nvisual standard error _____________\naverage audible reaction time _____________, and std dev ____________________\naudible standard error _____________

4. analysis\na. reaction time\nto begin with, we must relate a dropped distance to a time to fall that distance. using your knowledge of kinematics and free - fall motion, determine the time to fall a distance y. find this symbolically. show your work below. you should arrive at t = (\\frac{2y}{g})^{1/2}\nyou will determine the reaction time for each fall and record it in table 1. next, you will calculate the average reaction time and standard deviation for each data set, visual and audible\ntable 1. visual and audible reaction distances and related times\n|trial #|visual trials (m)|visual reaction time (s)|audible trials (m)|audible reaction time (s)|\n|----|----|----|----|----|\n|1| | | | |\n|2| | | | |\n|3| | | | |\n|4| | | | |\n|5| | | | |\n|6| | | | |\n|7| | | | |\n|8| | | | |\n|9| | | | |\n|10| | | | |\navg visual reaction time _____________, and std dev ____________________\nvisual standard error _____________\naverage audible reaction time _____________, and std dev ____________________\naudible standard error _____________

Answer

Explanation:

Step1: Recall free - fall kinematic equation

The kinematic equation for free - fall motion is $y = v_0t+\frac{1}{2}gt^2$. Since the initial velocity $v_0 = 0$ (dropped object), the equation simplifies to $y=\frac{1}{2}gt^2$.

Step2: Solve for time $t$

Starting from $y=\frac{1}{2}gt^2$, we first multiply both sides by 2 to get $2y = gt^2$. Then divide both sides by $g$: $\frac{2y}{g}=t^2$. Taking the square - root of both sides, we get $t=\sqrt{\frac{2y}{g}}=\left(\frac{2y}{g}\right)^{\frac{1}{2}}$.

Answer:

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