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 kinematic equation for free - fall

The kinematic equation for vertical motion under constant acceleration (free - fall, where the acceleration $a = g$ and initial vertical velocity $u = 0$) is $y=ut+\frac{1}{2}at^{2}$. Since $u = 0$, 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, we divide both sides by $g$: $t^{2}=\frac{2y}{g}$. Taking the square - root of both sides, we get $t=\sqrt{\frac{2y}{g}}=\left(\frac{2y}{g}\right)^{1/2}$.

The problem also asks for calculating average reaction time and standard deviation. However, since no data for visual and audible trials are given, we can't calculate the average reaction time and standard deviation. But the symbolic derivation of the time to fall a distance $y$ is shown above.

Answer:

The symbolic expression for the time $t$ to fall a distance $y$ is $t=\left(\frac{2y}{g}\right)^{1/2}$