Question

When a ruler falls vertically, 5 different persons catch it with different reaction times. What is the correct order of the distance travelled by the ruler for each person?
A. Person A: 0.20 s, B. Person B: 0.22 s, C. Person C: 0.18 s, D. Person D: 0.19 s, E. Person E: 0.21 s.

• A. C>D>A>E>B
• B. C>D>A>B>E
• C. B>E>A>D>C
• D. B>E>A>C>D

Hint:

You don't need to calculate the actual values of $h$. Since $h$ increases as $t$ increases, simply sorting the times in descending order gives you the descending order of distances.

Answer 1

The Correct Option is C

Step 1: Understanding the Topic:
This conceptual problem is related to "Kinematics," specifically motion under gravity. It describes a classic experiment used to measure human "reaction time." The distance an object falls from rest is a direct function of the time it is allowed to fall before being caught.
Step 2: Key Formulas and Approach:
We use the second equation of motion for an object falling under gravity from an initial velocity of zero: \[ s = ut + \frac{1}{2}gt^2 \] Since the ruler is dropped ($u = 0$): \[ s = \frac{1}{2}gt^2 \] This shows that distance $s$ is directly proportional to the square of time ($s \propto t^2$).
Step 3: Detailed Explanation:

Analyze the proportionality: Because $g$ and $1/2$ are constants, the distance $s$ increases as time $t$ increases. Specifically, as time grows, the distance grows even faster due to the squared relationship.
Sort the given times: To find the order of distances from largest to smallest, we simply need to sort the given reaction times in descending order.
B: 0.22 s (Longest)
E: 0.21 s
A: 0.20 s
D: 0.19 s
C: 0.18 s (Shortest)

Relate times to distances: Since B has the longest reaction time, the ruler falls the furthest for B. Since C has the shortest reaction time, the ruler falls the least for C.
Therefore, the descending order of distances is: $s_B>s_E>s_A>s_D>s_C$.
Step 4: Final Answer:
The correct order of distance travelled is B>E>A>D>C.