When aruler 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.

The correct answer is: B > E > A > D > C.

When a ruler is dropped and a person catches it after a reaction time $t$, the ruler falls freely under gravity. Starting from rest, the distance $d$ it travels during that time is given by the kinematic equation:

$d\; =\; \backslash frac\{1\}\{2\}\; g\; t^\{2\}$

Here $g$ is the acceleration due to gravity (≈ 9.8 m / s²). Since $g$ is the same for all five persons, the distance is directly proportional to the square of the reaction time:

$d\; \backslash propto\; t^\{2\}$

Therefore, a longer reaction time means a larger distance traveled.

List the given reaction times:

A: 0.20 s
B: 0.22 s
C: 0.18 s
D: 0.19 s
E: 0.21 s

Compute the squared times (or simply rank the times, since squaring preserves order):

A: (0.20)² = 0.0400
B: (0.22)² = 0.0484
C: (0.18)² = 0.0324
D: (0.19)² = 0.0361
E: (0.21)² = 0.0441

Now order the persons from the greatest distance (largest $t^\{2\}$) to the smallest:

1. B (0.22 s) – largest distance
2. E (0.21 s)
3. A (0.20 s)
4. D (0.19 s)
5. C (0.18 s) – smallest distance

This yields the sequence B > E > A > D > C, matching the provided correct option.