Functions/GenXdev.Helpers.Math.Physics/Get-FreeFallHeight.ps1
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################################################################################ <# .SYNOPSIS Calculates the height fallen during free fall for a given time duration. .DESCRIPTION This function calculates the distance fallen during free fall using a numerical method that accounts for air resistance and terminal velocity. The calculation uses small time steps to accurately model the physics of falling objects with realistic terminal velocity constraints. .PARAMETER DurationInSeconds The time duration of the fall in seconds for which to calculate the height. .PARAMETER TerminalVelocityInMs The terminal velocity in meters per second. Defaults to 53 m/s which is the typical terminal velocity for a human in free fall. .EXAMPLE Get-FreeFallHeight -DurationInSeconds 10 -TerminalVelocityInMs 53 Calculates the height fallen in 10 seconds with default human terminal velocity. .EXAMPLE Get-FreeFallHeight 5 Calculates the height fallen in 5 seconds using positional parameter and default terminal velocity. #> function Get-FreeFallHeight { [CmdletBinding()] [OutputType([double])] param( ################################################################################ [parameter( Mandatory = $true, Position = 0, HelpMessage = "The time duration of the fall in seconds" )] [double] $DurationInSeconds, ################################################################################ [parameter( Mandatory = $false, Position = 1, HelpMessage = ("The terminal velocity in meters per second " + "(default: 53 m/s for human)") )] [double] $TerminalVelocityInMs = 53 ################################################################################ ) begin { # define the acceleration due to gravity in meters per second squared $gravity = 9.81 # set up numerical integration parameters for accurate calculation $dt = 0.01 # initialize time tracking variable $time = 0 # initialize height accumulator $height = 0 # initialize velocity tracker $velocity = 0 Microsoft.PowerShell.Utility\Write-Verbose ( "Starting free fall calculation for ${DurationInSeconds} seconds " + "with terminal velocity ${TerminalVelocityInMs} m/s" ) } process { # perform numerical integration using small time steps while ($time -lt $DurationInSeconds) { # apply air resistance model by capping velocity at terminal velocity if ($velocity -ge $TerminalVelocityInMs) { # maintain constant terminal velocity when reached $velocity = $TerminalVelocityInMs } else { # accelerate under gravity when below terminal velocity $velocity += $gravity * $dt } # calculate distance traveled in this time step $height += $velocity * $dt # advance time by one step $time += $dt # prevent infinite loops with safety timeout if ($time -gt 1000) { Microsoft.PowerShell.Utility\Write-Error ( 'Calculation timeout exceeded 1000 seconds' ) return [double]0 } } Microsoft.PowerShell.Utility\Write-Verbose ( "Calculated fall height: ${height} meters" ) } end { # return the calculated height rounded to 2 decimal places as double return [double][Math]::Round($height, 2) } } ################################################################################ |