Free Fall Calculation: Accurate Distance in Seconds

[icon kid]

I'm a 3D artist and I'm making an animation that involves a free falling object. I know that, in a vacuum at least, an object will fall 32 feet during the first second; during the second second it'll fall 64 feet -- a total of 96 feet after only two seconds of free falling. The problem is that I need to know exactly how far an object has fallen at precise fractions of a second which is difficult to figure out unless someone knows of an easy, handy formula.

Each second of time is divided into 30 parts (frames). In this case I'm "keying" every other frame so the chart for this would look like the one below. In Frame 0 the object is at it's holding position but then it's let go to start falling. In Frame 2, the object has been falling for only a 15th of a second (0.0666 seconds) but I need to know exactly how far it traveled because I have to manually place the object at that point in space at that instant of time and then reposition it again and again after each 15th of a second passes, -- in order for the acceleration to be accurate and look natural.


-- 30 frames/second --

Frame 0 -- 0 seconds Distance = 0 feet
Frame 2 -- 1/15th second (0.0666) Distance = ? feet
Frame 4 -- 2/15th second (0.1332) Distance = ? feet
Frame 6 -- 3/15th second (0.1998) Distance = ? feet
Frame 8 -- 4/15th second (0.2664) Distance = ? feet
Frame 10 -- 5/15th second (0.3333) Distance = ? feet
Frame 12 -- 6/15th second (0.3996) Distance = ? feet
Frame 14 -- 7/15th second (0.4662) Distance = ? feet
Frame 16 -- 8/15th second (0.5328) Distance = ? feet
Frame 18 -- 9/15th second (0.5994) Distance = ? feet
Frame 20 -- 10/15th second (0.6666) Distance = ? feet
Frame 22 -- 11/15th second (0.7326) Distance = ? feet
Frame 24 -- 12/15th second (0.7992) Distance = ? feet
Frame 26 -- 13/15th second (0.8658) Distance = ? feet
Frame 28 -- 14/15th second (0.9324) Distance = ? feet
Frame 30 -- 1 second (1.0000) Distance = 32 feet

I found a free app that does free fall calculations but something seems wrong with the output I'm getting from it.

Here's a screen shot it.
http://www.jeffs-icons.com/free_fall_calc.gif

I'm using the calculation method for objects falling in a vacuum so the size (volume) and weight (mass) of the object as well as atmospheric parameters are irrelevant. In this case I'm solving for the distance fallen in a given amount of time. Time is expressed as numerical values only, and all values are interpreted as seconds, so a duration of "1 minute and 10 seconds" has to be entered as simply 70. To test the accuracy of this app before using its output, I entered a free fall time of one second. It should have given me a distance of roughly 32 feet for a one-second free fall. Instead it gave me 16.077 feet -- and that's far from the mark, almost half.

If you want to try this app yourself go to:
http://www.softpedia.com/get/Science-CAD/Free-Fall-Calculator.shtml
-- click the Free-Fall Calculator 1.0 download button
-- on the next page, right-click the "External Mirror 1" ZIP file and "Save target as." This will download a file called "Free-Fall.zip."

Does anyone know of either an online utility or a downloadable app that will give me the results I expect?

 

[Doc Al]

I'm a 3D artist and I'm making an animation that involves a free falling object. I know that, in a vacuum at least, an object will fall 32 feet during the first second; during the second second it'll fall 64 feet -- a total of 96 feet after only two seconds of free falling.

This is incorrect. After 1 second the object has fallen 16 feet; After 2 seconds it has fallen a total of 64 feet.

The problem is that I need to know exactly how far an object has fallen at precise fractions of a second which is difficult to figure out unless someone knows of an easy, handy formula.

The formula you need is (where time is in seconds and distance is in feet):
$$D = 1/2 g t^2 = 16 t^2$$

More accurately, the acceleration due to gravity (g) is closer to 32.15 ft/s^2 than 32 ft/s^2:
$$D = 1/2 g t^2 = 16.075 t^2$$

I found a free app that does free fall calculations but something seems wrong with the output I'm getting from it.

The problem is not with the app, but with your understanding of free fall. Read this: Freefall

 

[icon kid]

So I've misinterpreted the meaning of "32 feet per second squared" and the output of this free-fall calculator is reliable -- and easier to use than hand-working the formula which you graciously provided.
Thank you Doc Al.