Mathematics 7–10 · Years 7–8
Reaction time from a falling ruler: a formula, a table of values and class data
Number and algebra
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The idea
The distance a ruler falls before it is caught converts to a reaction time through the formula t = sqrt(2d/g), and repeating the catch gives a data set whose centre and spread can be compared between people or conditions.
What you need
- 30 cm ruler with millimetre markings per pair
- Recording table: trial, catch distance d (cm), reaction time t (s)
- Conversion table computed from t = sqrt(2d/g) with g = 9.8 m/s² (5 cm 0.101 s, 10 cm 0.143 s, 15 cm 0.175 s, 20 cm 0.202 s, 25 cm 0.226 s, 30 cm 0.247 s)
How to do it
- The catcher rests a forearm on the desk with the hand over the edge, thumb and index finger 3 cm apart. The partner holds the ruler so the zero mark hangs level with the top of the catcher's thumb.
- Without warning the partner releases the ruler; the catcher closes finger and thumb. Read the distance at the top of the thumb to the nearest 0.5 cm.
- Repeat for 10 catches; discard a trial only if the ruler was missed entirely (record it as a miss).
- Convert each distance to a time by substituting into t = sqrt(2d/g), keeping d in metres and g = 9.8 m/s², and check against the printed table.
- Compute the median and range of the 10 times; swap roles and repeat.
- Compare the class distribution of medians for the dominant and non-dominant hand, or with eyes on the ruler versus responding to the partner's spoken go.
What you should see
Catch distances of 10 to 25 cm give reaction times of 0.143 to 0.226 s; a catch at 20 cm gives 0.202 s and at 30 cm gives 0.247 s. The Franklin Institute's chart, rounded to two decimal places, agrees at 5, 10, 20, 25 and 30 cm and gives 0.18 s at 15 cm where the formula gives 0.175 s, so the two tables agree within 0.01 s. Because t grows with the square root of d, doubling the distance from 10 to 20 cm raises t by a factor of 1.41, not 2. The Franklin Institute notes that practice shortens reaction time, so early catches may be slower than later ones. The learner knows it worked when their converted times agree with the printed table and the median of a repeat set of 10 is close to the first.
What changes
- What you change
- condition (hand used, or visual versus spoken cue)
- What you measure
- reaction time
- What you keep the same
- same ruler
- same starting gap between finger and thumb
- forearm resting on the desk
- no countdown
Common misconceptions
Each of these ideas is wrong, and the activity is a chance to test it.
- Reaction time is proportional to the distance the ruler falls.
- A single trial measures reaction time.
- A longer ruler makes people slower.
Safety card
Hazards
- ruler dropped on a foot
Controls
- catch over the desk, not over the floor
Note
No chemicals or heat are used, so the NSW Department of Education Chemical Safety in Schools package does not apply; ordinary classroom supervision.
Curriculum references
The NSW syllabus outcomes and Australian Curriculum v9 codes this activity supports. They are references, not a verified or complete curriculum alignment.
- Mathematics K–10 Syllabus (2022), Stage 4 Algebraic techniques; page read 2026-09-22MA4-ALG-C-01
- Mathematics K–10 Syllabus (2022), Stage 4 Data analysis; page read 2026-09-22MA4-DAT-C-02
- Australian Curriculum v9AC9M7A01AC9M7ST01AC9M7ST02
Sources
The pages the author read to write this activity.