Problem

A ball is thrown vertically upward, which is the …

02:00

Problem 45 Medium Difficulty

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 milliseconds (ms). Calculate the distances $d_{1}, d_{2},$ and $d_{3} .$

Answer

$\begin{aligned} d_{1} &=0.01764 \mathrm{m} \\ d_{2} &=0.07056 \mathrm{m} \\ d_{3} &=0.15876 \mathrm{m} \end{aligned}$

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Physics 101 Mechanics

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Video Transcript

can this problem were? Given what? They describe the device where you can calculate your reaction time by dropping, um, a piece of cardboard and they give us three distances or they show us that distance. One corresponds to a time of 60 milli seconds. Distance to corresponds to a time of 120 milliseconds in distance. Three corresponds to a time of 180 milliseconds. So it's our job to calculate what those three distances are. How, how far will something fall in each of these three time intervals? So we're gonna use the equation Vertical distances via V, not T plus 1/2 times acceleration times t squared. But in this case, our acceleration will always be G or 9.8 meters per second squared. Since everything in this problem is moving down, we can just call the direction down positive. So we don't need to worry about any negative signs. So for the 1st 1 will do just distance. One on the vertical distance is V not T plus 1/2 9.8 10 t squared. So our initial velocity for all three of these cases is zero. So that first term can be, um, canceled out. We have 1/2 9.8 times T square. Now we just have to remember that time has to be in seconds. Not Milli seconds. Amily. Second is 1000 of a second, so I can divide my 10000.6 5000. I mean, my 60 by 1000 I get 10000.6 seconds. So plugging my numbers in here, I get a distance of 0.1764 meters. And that would be my Why one or my? What they call d one. Okay. For the 2nd 1 we're gonna double our distance. I'm sorry, double our time. So we're going to calculate our new distance. So why is equal to zero plus 1/2? 9.8? Tent city squared and R T this time is 120 milliseconds. So that's 1200.120 seconds squared. So plugging our numbers into this we have 0.7056 meters for what we call d to the 3rd 1 is going to be the same exact process. Why is equal to zero plus 1/2 9.8 meters per second squared times 180 milliseconds, which is 1800.180 seconds squared and plugging our numbers into this one. I'll call this d three. It is 30.15876 Okay, so we have three answers 0.1764 0.7056 and 0.1576

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