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 Concept:
The distance a ruler falls ($h$) under gravity depends on the square of the time ($t$) it takes to catch it. A longer reaction time allows the ruler to fall a greater distance.

Step 2: Key Formula or Approach:
Using the second equation of motion for an object dropped from rest ($u=0$): \[ h = \frac{1}{2}gt^2 \] Since $g$ is constant, $h \propto t^2$.

Step 3: Detailed Explanation:
1. The distance ($h$) is directly proportional to the square of the reaction time. 2. Therefore, the person with the longest reaction time will see the greatest distance travelled by the ruler. 3. Ranking reaction times from longest to shortest: - B (0.22 s) $>$ E (0.21 s) $>$ A (0.20 s) $>$ D (0.19 s) $>$ C (0.18 s) 4. Corresponding distance order: $h_B > h_E > h_A > h_D > h_C$.

Step 4: Final Answer:
The correct order of distance is B > E > A > D > C.