How this instrument works
Drop something — no throw, no push — and gravity accelerates it at a constant 9.80665 m/s², the standard value used in engineering the world over. From that single constant, two clean results follow: the fall time grows with the square root of the height, and the impact velocity grows in proportion to the time. Double the height and the fall takes only 41% longer; the landing, though, is 41% faster.
This sheet ignores air resistance, which is honest for dense objects over household-to-building heights and increasingly wrong for feathers, paper, and anything falling far enough to approach terminal velocity. The instrument tells you what ideal physics says; the atmosphere negotiates the rest.
- Choose the direction on the dial: start from the drop height, or from a measured fall time.
- Enter your figure in any unit — metres, feet, even miles for the morbidly curious.
- Read the computed pair; the field being solved shows its rearranged formula in the working block.
Worked example — the 45-metre cliff
A stone dropped from a 45-metre cliff — about a 14-storey building. Fall time: t = √(2 × 45 ⁄ 9.80665) = √9.177 = 3.03 seconds. Impact velocity: v = 9.80665 × 3.03 = 29.7 m/s, which the unit menu will convert to 107 km/h or 66 mph.
Three seconds sounds long until you stand somewhere high with a stopwatch. It is also the classic field method in reverse: time a dropped pebble into a well, switch this instrument to 'From time', and it returns the depth — 3 seconds of fall means about 44 metres.
Questions
Does the object's weight matter?
Not in the ideal case — a hammer and a coin dropped together land together, as Apollo 15 demonstrated on the Moon. Weight only enters through air resistance, which slows light, draggy objects more. For a rock off a bridge, this sheet is accurate; for a beach ball, it is optimistic.
When does air resistance start to matter?
As a rule of thumb, once speeds pass roughly 20–30 m/s (after about 20–45 m of fall for compact objects) drag begins shaving noticeable percentages off. A skydiver stops accelerating entirely near 55 m/s. Beyond a few seconds of fall, treat these figures as upper bounds.
Why 9.80665 and not 9.8 or 10?
9.80665 m/s² is the conventional standard gravity fixed by international agreement in 1901 — the value engineering tables assume. Real local gravity varies by about ±0.03% between the equator and the poles; the standard value is the honest middle and matches published references.
Can I use this for something thrown downward?
No — these formulas assume the object starts at rest. A throw adds an initial velocity term (v₀), which changes both equations. A projectile-motion instrument with initial velocity is on the board in this series.