A. Person A has reaction time of $0.20 \text{ s}$.
B. Person B has reaction time of $0.22 \text{ s}$.
C. Person C has reaction time of $0.18 \text{ s}$.
D. Person D has reaction time of $0.19 \text{ s}$.
E. Person E has reaction time of $0.21 \text{ s}$.
What is the correct order of the distance travelled by the ruler for each person ?
Understanding Ruler Fall Distance and Reaction Time
When a ruler falls vertically from rest, the distance it travels ($d$) is determined by the time it is in the air. This motion is governed by the laws of kinematics under constant acceleration due to gravity ($g$).
Kinematic Equation for Distance
The distance fallen by an object starting from rest is given by the equation:
$d = \frac{1}{2}gt^2$
where $g$ is the acceleration due to gravity and $t$ is the time of fall. In this problem, the time of fall is the reaction time of each person catching the ruler.
Relationship Between Distance and Reaction Time
Since $g$ is constant ($9.8 \text{ m s}^{-2}$), the distance traveled ($d$) is directly proportional to the square of the reaction time ($t^2$). For positive reaction times:
- A longer reaction time ($t$) results in a greater distance traveled ($d \propto t^2$).
- Therefore, to find the order of distances travelled, we need to order the reaction times from longest to shortest.
Ordering Reaction Times
The given reaction times are:
- Person A: $0.20 \text{ s}$
- Person B: $0.22 \text{ s}$
- Person C: $0.18 \text{ s}$
- Person D: $0.19 \text{ s}$
- Person E: $0.21 \text{ s}$
Ordering these times from largest to smallest:
- Person B: $0.22 \text{ s}$
- Person E: $0.21 \text{ s}$
- Person A: $0.20 \text{ s}$
- Person D: $0.19 \text{ s}$
- Person C: $0.18 \text{ s}$
Determining the Order of Distances
Since the distance travelled is directly proportional to the reaction time (or its square), the order of distances will match the order of reaction times from longest to shortest.
Thus, the order of distances travelled is:
Distance for B > Distance for E > Distance for A > Distance for D > Distance for C
This corresponds to the order: B > E > A > D > C.
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