d3 goes from the asterisks to 180 ms d2 goes from the asterisks to 120 ms d1 goe

Question

d3 goes from the asterisks to 180 ms

d2 goes from the asterisks to 120 ms

d1 goes from the asterisks to 60 ms

I have answers for d2 and d3 as below, but d1 below is wrong in my homework. Can someone please show correct answer for d1?

d1= 0.018 m WRONG

d2= 0.071 m CORRECT

d3= 0.16 m CORRECT

Please let me know how you get the answer.
thank you :)

The drawing shows a device that you can make with a piece of cardboard, which can be used to measure a person's reaction time. Hold the card at the top and suddenly drop it. Ask a friend to try to catch the card between his or her thumb and index finger. Initially, your friend's fingers must be level with the asterisks at the bottom. By noting where your friend catches the card, you can determine his or her reaction time in miliseconds (ms). Calculate the distances d1, d2, and d3 for reference: d3 goes from the asterisks to 180 ms d2 goes from the asterisks to 120 msd1 goes from the asterisks to 60 ms I have answers for d2 and d3 as below, but d1 below is wrong in my homework. Can someone please show correct answer for d1? d1= 0.018 m WRONG d2= 0.071 m CORRECT d3= 0.16 m CORRECT

Explanation / Answer

The board is freely falling and the initial velocity of that is zero(0) as the person just leaves it without giving it any velocity.

we know S = u*t + a*(t^2)/2

and u = 0 here so S = a*(t^2)/2

where S is distance traveled and t time taken with acceleration a(acceleration due to gravity = 10m/s^2)

so calculating using that formula

for d1 time = 60ms = 60*(10^-3) seconds

S = 10 * 60 *60 *(10^-6)/2 = 18 * 10^-3 m = 0.018m

d2 time = 120ms = 120*(10^-3) seconds

S = 10 * 120 *120 *(10^-6)/2 = 72 *10^-3m = 0.072m

for d3 time = 180ms = 180*(10^-3) seconds

S = 10 * 180 *180 *(10^-6)/2 = 162 * 10^-3m = 0.162m

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