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?)

To determine the distances for the different reaction times, we need to analyze the given information and look for patterns.

Let's start with the 50.0 ms mark. This mark represents the reaction time of 50 milliseconds. Since the mark is placed where you pinch the strip, it indicates the distance your thumb and forefinger would travel in 50 milliseconds.

Now, let's consider the other marks for (b) 100, (c) 150, (d) 200, and (e) 250 ms. To find these distances, we will look for a pattern in the times and distances.

If we assume that the reaction times (in milliseconds) are directly proportional to the distances traveled by your thumb and forefinger, we can use the formula:

distance ∝ time

This means that if the time doubles, the distance should also double. So, if the 100 ms marker is 2 times as far from the dot as the 50 ms marker, the same ratio should hold for the other markers as well.

Now, let's calculate the distances for each of the given reaction times:

(a) 50.0 ms (starting point)
(b) 100 ms is twice the distance of 50 ms
(c) 150 ms will also be twice the distance of 100 ms
(d) 200 ms will again be twice the distance of 150 ms
(e) 250 ms will follow the pattern and be twice the distance of 200 ms

Hence, we can conclude that the distances from the lower dot for each reaction time are as follows:

(a) 50.0 ms mark: Starting point
(b) 100 ms mark: 2 times the distance of the 50 ms mark
(c) 150 ms mark: 2 times the distance of the 100 ms mark
(d) 200 ms mark: 2 times the distance of the 150 ms mark
(e) 250 ms mark: 2 times the distance of the 200 ms mark

By following this pattern of doubling the distances, you can determine the placement of the different reaction time marks on the cardboard strip.