Free Fall Time Game
Drop it from this height. How many seconds until it hits the ground?
About Fall Time
Fall Time shows an everyday object, a small picture and a height marker, and asks how long it needs to hit the ground after being dropped. Heights go from half a meter, about the edge of a table, to 300 meters, taller than most skyscrapers. You slide to a time in seconds between 0.1 and 10.
The difficulty is that falling does not feel linear. A drop from 20 meters is not ten times slower than a drop from 2 meters; it is only about three times slower. The fall time grows with the square root of the height, and that surprise is exactly what the game helps you internalize. The slider is logarithmic so that both short and long times are easy to set.
How to play
- Read the height next to the object. Heights are given in meters.
- Think of how long a fall of that height lasts. A good reference is that a drop of 5 meters takes about 1 second.
- Slide to your estimate in seconds; the plus and minus buttons give fine control.
- Lock in. The object falls on screen so you can compare the real time with your guess.
An object is dropped from the height shown. Slide to how many seconds it takes to hit the ground. Ignore air resistance. The slider is logarithmic.
How scoring works
The score is based on the ratio between your estimate and the true time, on a logarithmic scale. That means that 2 seconds when the truth is 1 second costs as much as 0.5 seconds. A perfect answer is worth 100 and the score drops to 0 at a factor of about 2.2 on level 1 and 1.6 on level 10.
The true time follows from t equals the square root of 2h divided by g, with g being 9.81 meters per second squared, and air resistance is ignored. On the first three levels heights stay between 1 and 30 meters; later the full range up to 300 meters is used. The timer is 14 seconds on level 1 and 11 seconds on level 10.
What it trains
Fall Time trains your sense of the speed of falling objects, a skill that shows up when you catch a falling glass, judge the depth of a well from the splash, or decide whether a jump is safe. It also teaches an important idea: some relationships are neither linear nor exponential, but follow a square root.
It also gives you practice with logarithmic thinking, comparing values by ratio instead of difference. That is the same way our senses work for loudness, brightness and weight.
Tips for a higher score
- Memorize the milestones: 5 meters is about 1 second, 20 meters about 2 seconds, 45 meters about 3 seconds and 80 meters about 4 seconds. Each extra second needs more and more height.
- To get from a height to a time, take the square root and divide by about 4.5. For 100 meters, the root is 10, so the time is a bit over 4.5 seconds.
- Quadruple the height to double the time. 5 meters takes 1 second, 20 meters takes 2 seconds and 80 meters takes 4.
- Do not use experience with parachutes or paper. In the game there is no air resistance, so a feather and a rock fall together.
- Keep in mind that tabletop drops are quick. A fall from 1 meter takes less than half a second, which is about the time you need to see it coming.
The idea behind it
Galileo is credited with showing, around 1600, that falling bodies accelerate uniformly and that, apart from air resistance, heavy and light objects fall equally fast. In 1971 astronaut David Scott demonstrated it on the Moon by dropping a hammer and a feather together; both landed at the same moment because there is no air there.
On Earth, air resistance matters for light or fast objects. A skydiver reaches a terminal velocity of about 55 meters per second, and an apple dropped from 300 meters would be noticeably slower than the vacuum value used in the game. For the heights of everyday life, the vacuum formula is a very good approximation.
Frequently asked questions
Does a heavier object fall faster?
Without air resistance, no. All objects accelerate at the same rate. In the game, the picture of the object is only decoration and has no effect on the answer.
Why is the slider logarithmic?
Times between 0.3 and 8 seconds span a wide range, and what matters is the ratio, not the difference. A log slider gives you the same precision at both ends.
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