a simple device for measuring your reactiontime. It consists of a cardboard stri
ID: 2028958 • Letter: A
Question
a simple device for measuring your reactiontime. It consists of a cardboard strip marked with a scale and twolarge dots. A friend holds the strip vertically, with thumb andforefinger at the dot on the right in the figure below. You thenposition your thumb and forefinger at the other dot (on the left inthe figure), being careful not to touch the strip. Your friendreleases the strip, and you try to pinch it as soon as possibleafter you see it begin to fall. The mark at the place where youpinch the strip gives your reaction time.a)How far from the lower dot should you place the 50.0 ms mark?
b)How much higher should the mark for 100 be? (For example, should the 100 ms marker be two times as far from the dot as the 50 ms marker?)
c)How much higher should the mark for 150 be?
d)Can you find any pattern in the answers?
Explanation / Answer
We want to find the distance the paper falls in 50, 100, and 150 ms. The paper accelerates due to gravity. There is a nice equation for constant speed distance = rate times time or D = RT Gravity, g, changes the speed so we use average rate times time. If it wasn't moving when we started, it will be going gt after t seconds. Since it is not moving when the friend lets go, the starting speed is 0. Therefore the average speed = (0 + gt)/2 So rate = gt/2 distance = gt/2*t or (1/2)gt^2 a) 50ms dot should be (1/2)(9.8m/s^2)(.05s)^2 = 0.006125m or 6.1 mm from the lower dot. b) 100ms dot should be (1/2)(9.8m/s^2)(2*.005s)^2 = 24.4 mm from the lower dot, or four times as far. c) 150 ms dot should be (1/2)(9.8m/s^2)(3*.005s)^2 = 55 mm from the lower dot, or nine times as far. d) 100ms = 2*50ms and disance is 4x, 150ms = 3*50ms and distance is 9x so the pattern is that the ratio is squared to get the distance. This is due to the time squared in the equation d = (1/2)gt^2
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