Wolfram Function Repository

Instant-use add-on functions for the Wolfram Language

Function Repository Resource:

 TimeToFallFormula

Source Notebook

Calculate the time to fall from a specified height

Contributed by: Julián Laverde

ResourceFunction["TimeToFallFormula"][h]

returns the time taken for an object to fall vertically from a distance h without drag.

ResourceFunction["TimeToFallFormula"][h,assoc]

returns the time taken for an object to fall vertically from a distance h with drag parameters in the Association assoc.

ResourceFunction["TimeToFallFormula"][property]

returns the specified property of the time to fall formula.

Details and Options

The height h can be a number or a Quantity with length units. If given only as a number, the value is assumed to be in meters.
In ResourceFunction["TimeToFallFormula"][h, assoc], assoc can include the following basic elements:
"DragCoefficient"0.5resistance of the object falling in the fluid
"Area"20 cm2the object's projected area
"Mass"3 kgthe object's mass
"Density"1.29 kg/m3the fluid's density
The "DragCoefficient" can be a number greater than 0.
The object's projected "Area" can be a number or a Quantity with area units. If given only as a number, the value is assumed to be in square centimeters.
The object's "Mass" can be a number or a Quantity with mass units. If given only as a number, the value is assumed to be in kilograms.
The fluid's "Density" can be a number or a Quantity with density units. If given only as a number, the value is assumed to be in kilograms over cubic meters.
ResourceFunction["TimeToFallFormula"] can take the option "Gravity" to specify the gravitational acceleration "g". If unspecified, it is assumed to be equal to the "StandardAccelerationOfGravity".
Properties include:
"FormulaWithDrag"equation for time to fall with drag
"FormulaWithoutDrag"equation for time to fall without drag
"QuantityVariableNames"English names for all variables

Examples

Basic Examples (2) 

Calculate the time to fall without drag:

In[1]:=
ResourceFunction["TimeToFallFormula"][Quantity[100, "Meters"]]
Out[1]=

Calculate the time to fall considering drag:

In[2]:=
ResourceFunction["TimeToFallFormula"][ Quantity[200, "Meters"], <|"DragCoefficient" -> 0.5, "Area" -> Quantity[20, ("Centimeters")^2], "Mass" -> Quantity[2.89, "Kilograms"], "Density" -> Quantity[1.5, ("Kilograms")/("Meters")^3]|>]
Out[2]=

Scope (3) 

Show the formula used with drag:

In[3]:=
ResourceFunction["TimeToFallFormula"]["FormulaWithDrag"]
Out[3]=

and without drag:

In[4]:=
ResourceFunction["TimeToFallFormula"]["FormulaWithoutDrag"]
Out[4]=

Find the name of the quantity variables used by TimeToFallFormula:

In[5]:=
ResourceFunction["TimeToFallFormula"]["QuantityVariableNames"]
Out[5]=

TimeToFallFormula is listable:

In[6]:=
ResourceFunction["TimeToFallFormula"][{100, 200, 300}]
Out[6]=

Options (1) 

Gravity (1) 

Use "Gravity" to specify the value of the gravity used:

In[7]:=
ResourceFunction["TimeToFallFormula"][Quantity[250, "Feet"], "Gravity" -> Entity["PlanetaryMoon", "Moon"][ EntityProperty["PlanetaryMoon", "Gravity"]]]
Out[7]=

Properties and Relations (1) 

Use Quantity to specify the units of the inputs:

In[8]:=
ResourceFunction["TimeToFallFormula"][Quantity[30, "Feet"]]
Out[8]=

Neat Examples (2) 

Plot the time that it would take to fall from the highest mountain of each continent:

In[9]:=
highestMountainHeights = EntityValue[ EntityClass[ "Mountain", {EntityProperty["Mountain", "Elevation"] -> TakeLargest[1], EntityProperty["Mountain", "Continent"] -> EntityClass["GeographicRegion", "Continents"]}], "Elevation", "EntityAssociation"]; highestMountainsTimeToFall = ResourceFunction["TimeToFallFormula"][highestMountainHeights]; GeoBubbleChart[ MapIndexed[Tooltip[#1, Column[{#2[[1, 1]], #1}]] &, highestMountainsTimeToFall], BubbleSizes -> {.1, .4}]
Out[11]=

Plot the time that it would take to fall the height of the Empire State Building on each planet in the solar system:

In[12]:=
BarChart[ResourceFunction["TimeToFallFormula"][ Entity["Building", "EmpireStateBuilding::h583b"]["Height"], "Gravity" -> #] & /@ EntityClass["Planet", All]["Gravity"], ChartStyle -> EntityValue[ EntityClass["Planet", All][EntityProperty["Planet", "Color"]], "Value"], ChartLabels -> EntityClass["Planet", All]["Name"], TargetUnits -> Automatic, AxesLabel -> "Time (s)"]
Out[12]=

Publisher

WolframSpecialProjects

Version History

  • 1.0.0 – 01 March 2021

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