Experiment 10: Ruler Drop — Reaction Time

How fast are you, really? Reaction time is the delay between a stimulus and your response: light hits the retina, signals travel to the visual cortex, the brain decides, and motor signals travel down to the hand. That loop takes roughly a fifth of a second — and you can measure it with a falling ruler and one physics equation, because a falling object accelerates predictably. The Virtual Lab: Ruler Drop — Reaction Time Tester on this page gives you unlimited drops; the bench version needs only a partner and a 30 cm ruler.

The science behind the practical

For an object falling from rest under gravity, distance and time are linked by d = ½gt², where g ≈ 9.8 m/s². Rearranged, t = √(2d/g). The ruler converts time into distance: a slow catch lets it fall further. Because the equation has a square root, distance is not proportional to time — double the distance means only about 1.41× the time (√2), a point that catches out many first analyses. A typical visual reaction time is 0.19–0.25 s, corresponding to catches around 18–30 cm. Reaction time worsens with distraction and fatigue and improves modestly with practice — the nervous system does not get faster signals, but the decision stage gets slicker.

Variables, controls and fair testing

Use a light plastic ruler and keep fingers clear of the drop path.

Running the investigation well

The dropper must not signal the drop — no counting down, no flinching first, and the release moment randomised within a few seconds. The catcher's fingers hover at the 0 cm mark without touching the ruler. Record the distance at the *top of the thumb* consistently. Five trials minimum per condition: single drops are noisy, and the odd flinch or super-catch would dominate a lone reading. In the simulator, run a long series and notice how your own scores cluster — the spread of your times is itself data about consistency.

Worked example: a sample investigation

Catch distances (cm) for one student, five trials per condition:

Analysing the sample data

Step 1 — mean distances. Dominant: (18 + 22 + 15 + 20 + 17) ÷ 5 = 92 ÷ 5 = 18.4 cm. Non-dominant: (24 + 27 + 21 + 26 + 23) ÷ 5 = 121 ÷ 5 = 24.2 cm. Warned: (16 + 15 + 18 + 14 + 17) ÷ 5 = 80 ÷ 5 = 16.0 cm.

Step 2 — convert to time with t = √(2d/g), using metres. Dominant: √(2 × 0.184 ÷ 9.8) = √0.0376 = 0.194 s. Non-dominant: √(2 × 0.242 ÷ 9.8) = √0.0494 = 0.222 s. Warned: √(2 × 0.160 ÷ 9.8) = √0.0327 = 0.181 s.

Step 3 — interpret. The non-dominant hand cost about 0.028 s (28 ms) — the motor pathway to the less-practised hand is slower to organise. A warning saved about 13 ms, because the brain could pre-load the response. Note the trap avoided: 24.2 cm is 32% more distance than 18.4 cm, but only 15% more *time* — the square root matters.

Conclusion and evaluation

Conclusion: mean reaction times were 0.194 s (dominant), 0.222 s (non-dominant) and 0.181 s (warned), all in the expected human range. Reaction time is condition-dependent: the same nervous system responds faster with its practised hand and with advance warning.

Evaluation: five trials still leave a visible spread (15–22 cm for the dominant hand), so the mean carries uncertainty; a partner's unconscious pre-drop cues can contaminate "unwarned" trials. Improvements: ten trials per condition, dropper standing behind a screen, a phone-based reaction timer as a cross-check, and reporting the median alongside the mean.

Safety and ethics

Physically trivial — a falling plastic ruler — but use a light ruler and keep the drop zone clear of faces. Human-subject ethics still apply: results are personal performance data, so share them by agreement, and never rank classmates publicly by name. Anyone can opt to be the dropper instead.

Common mistakes

• Converting with d in centimetres inside the formula — g is in m/s², so d must be in metres.
• Assuming distance ∝ time and reporting "32% slower" instead of converting properly.
• Letting the catcher watch the dropper's hand tense, turning a reaction test into an anticipation test.
• Using one trial per condition and treating noise as a finding.

Exam Experience

Question 1 — Analysis (4 marks). A student catches the ruler at a mean distance of 20.0 cm. (a) Calculate the reaction time. (b) Another student catches at 45.0 cm; without calculating fully, state whether their time is more or less than double the first student's, and why. *Scoring guide:* (a) t = √(2 × 0.200 ÷ 9.8) = √0.0408 = 0.202 s (1 mark method, 1 mark answer). (b) Less than double (1 mark): distance scales with t², so 2.25× the distance is only √2.25 = 1.5× the time (1 mark).

Question 2 — Evaluation and design (4 marks). A student tests "energy drinks speed up reactions" by dropping the ruler for a friend before and after a drink, always in that order. Identify two flaws and improve the design. *Scoring guide:* Flaws (1 mark each): practice effect confounds the order (later trials are better anyway); no placebo/blinding, so expectation effects are possible; one subject (accept any two). Improvements (up to 2 marks total): randomise or counterbalance order, use a decaffeinated placebo with the taster unaware, more subjects, fixed trial counts.

Multiple choice 1. A catch at 30 cm corresponds to a reaction time of about: A) 0.12 s B) 0.25 s C) 0.55 s D) 3.0 s. *Key: B.* t = √(2 × 0.30 ÷ 9.8) = √0.0612 ≈ 0.247 s. A would be a ~7 cm catch; C confuses the formula with d = gt.

Multiple choice 2. Reaction time improves slightly with practice mainly because: A) nerve signals travel faster B) the brain's decision and motor organisation become more efficient C) the ruler falls more slowly D) the eyes see the ruler sooner. *Key: B.* Conduction speeds are fixed; practice streamlines processing and preparation, not the physics (C) or the stimulus (D).

Going deeper: why 0.2 seconds matters at 50 km/h

Reaction time leaves the lab every time someone drives. A car at 50 km/h travels at 50 ÷ 3.6 = 13.9 m/s. In the worked example's dominant-hand time of 0.194 s, that car covers 13.9 × 0.194 = 2.7 metres before the driver's foot even moves — the "thinking distance" on road-safety charts. At a more typical tired 0.25 s it is 3.5 m; at a phone-distracted 0.40 s, 5.6 metres — longer than the car itself, travelled blind. Braking distance comes on top of these, which is why road-safety campaigns are measured in your ruler-drop units whether they say so or not.

The senses differ, too: auditory reaction times average roughly 0.17 s, faster than visual (~0.20 s), because the auditory pathway to the cortex is shorter; touch sits between. Sprint starts exploit this — athletes react to the gun, not to a light — and false-start rules in athletics disqualify reactions under 0.10 s on the grounds that no human nervous system completes the loop that fast: sub-0.10 means anticipation, not reaction, a judgement your own "warned" condition (0.181 s) puts in perspective.

Finally, notice the floor under all your measurements: even a perfect catcher cannot beat the physics of the drop itself plus nerve conduction — the ruler drop measures a *system* (eye, brain, hand, gravity), and naming what a measurement includes is the beginning of trusting it.

A second look: the median defends you from your own flinches

Your five dominant-hand catches (15, 17, 18, 20, 22 cm) give a mean of 18.4 cm and a median (middle value) of 18 cm — close together, because the data are well behaved. Now add a sixth trial: an 8 cm catch where you flinched and grabbed early by luck. The mean of [8, 15, 17, 18, 20, 22] falls to 100 ÷ 6 ≈ 16.7 cm — apparently a big improvement, and entirely fake. The median of the same six values is (17 + 18) ÷ 2 = 17.5 cm: it moved a little, honestly. The median is *robust* — resistant to extreme values — because it cares only about rank, not size; the mean uses every millimetre of every value, including the fluke. Reaction-time data are full of flukes in both directions (flinch-catches and daydream drops), which is why serious protocols report medians or trim extremes, and why your exam answers should reach for the median when a dataset has a wild value wearing no explanation. Choosing the right average is not pedantry; it is choosing not to be fooled by your own fastest accident.

Final check: practice, measured honestly

Does practice really help, or does it just feel that way? The same student re-ran the dominant-hand protocol after five days of casual practice: mean catch distance fell from 21.6 cm to 17.9 cm. Convert both: day 1, t = √(2 × 0.216 ÷ 9.8) = √0.0441 = 0.210 s; day 5, t = √(2 × 0.179 ÷ 9.8) = √0.0365 = 0.191 s. A gain of 19 milliseconds — about 9% — from five days. Real, but modest, and notice its shape: most of the gain came early (the warm-up trials of day 1 were the worst of all), after which returns diminished. Skill acquisition follows the same curve as mould growth and seedling height in this course: steep learning, then a plateau set by the hardware. The nervous system's conduction speeds never changed; what practice bought was preparation — the response pre-loaded, the decision pre-made. That is also the honest limit of "training" claims for reaction apps, and your data, not their marketing, arbitrate it.