Free Fall problem with a reaction time strip

[Wilcho]

Figure 2-42 shows a simple device for measuring your reaction time. It consists of a cardboard strip marked with a scale and two large dots. A friend holds the strip vertically, with thumb and forefinger at the dot on the right in Figure 2-42. You then position your thumb and forefinger at the other dot (on the left in Figure 2-42), being careful not to touch the strip. Your friend releases the strip, and you try to pinch it as soon as possible after you see it begin to fall. The mark at the place where you pinch the strip gives your reaction time. (a) How far from the lower dot should you place the 50.0 ms mark? How much higher should you place the marks for (b) 100, (c) 150, (d) 200, and (e) 250 ms? (For example, should the 100 ms marker be 2 times as far from the dot as the 50 ms marker? If so, give an answer of 2 times. Can you find any pattern in the answers?)



x-x0 = V0t - 1/2gt^2



The above equation is the equation I attempted to use to solve the problem. So far i got x = -4.9(50/1000)^2. I divided 50 by a 1000 to convert millisecond to seconds because gravity's unit is m/s. Therefore when you multiply the time with the gravitational force to get the distance. Then i got .01225 but i got the answer wrong for a. Then it gives an example that says the 100ms marker be 2 times as far from the dot as the 50ms marker. Is this example suppose to be true? or just an example?. Also, I got the units wrong b,c,d,e but i got a right, which is in meters.

 

[kuruman]

Start with Δx=(1/2)gt². This represents the distance between the initial "dot" and the part of the strip that is next to your fingers as it falls. You say you found the first distance correctly to be 1.225 cm (0.01225 m) and I believe that is correct.

Let us represent this distance with the symbol d and the time of 50 ms with the symbol t₀. Then we have

d=(1/2)gt₀²

Now the next mark (100 ms) is 2t₀. If you replace t with 2t₀ in the original equation for Δx, what do you get for the distance? What number times d is that?

 

[Wilcho]

Oh i see, thank you very much.