Functions/GenXdev.Helpers.Math.Physics/Get-FreeFallTime.ps1
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################################################################################ <# .SYNOPSIS Calculates the time it takes for an object to fall a specified distance. .DESCRIPTION This function calculates the time it takes for an object to fall from a given height, taking into account terminal velocity due to air resistance. It uses a numerical method with small time steps for accurate calculation. .PARAMETER HeightInMeters The initial height of the falling object in meters. .PARAMETER TerminalVelocityInMs The terminal velocity of the falling object in meters per second. Default value is 53 m/s, which is the approximate terminal velocity of a human in free fall. .EXAMPLE Get-FreeFallTime -HeightInMeters 100 # Returns the time in seconds for an object to fall 100 meters with default # terminal velocity .EXAMPLE Get-FreeFallTime 500 45 # Returns the time in seconds for an object to fall 500 meters with a terminal # velocity of 45 m/s #> Function Get-FreeFallTime { [OutputType([double], [int])] [CmdletBinding()] param ( ######################################################################## [parameter( Position = 0, Mandatory = $true, HelpMessage = "The initial height of the falling object in meters" )] [double]$HeightInMeters, ######################################################################## [parameter( Position = 1, Mandatory = $false, HelpMessage = "The terminal velocity of the falling object in m/s" )] [double]$TerminalVelocityInMs = 53 # Default human terminal velocity in m/s ######################################################################## ) begin { # define the acceleration due to gravity in m/s^2 [double] $gravity = 9.81 # set up time step for numerical calculation in seconds [double] $dt = 0.01 # Time step in seconds # initialize variables for the simulation [double] $height = $HeightInMeters [double] $velocity = 0 [double] $time = 0 Microsoft.PowerShell.Utility\Write-Verbose ( "Calculating free fall time from height: $HeightInMeters m with " + "terminal velocity: $TerminalVelocityInMs m/s" ) } process { # simulate the fall until the object reaches the ground while ($height -gt 0) { # apply simplified air resistance model by capping at terminal velocity if ($velocity -ge $TerminalVelocityInMs) { $velocity = $TerminalVelocityInMs } else { # increase velocity due to gravity $velocity += $gravity * $dt } # update height based on current velocity $height -= $velocity * $dt # increment time counter $time += $dt # add safety check to prevent infinite loops if ($time -gt 1000) { Microsoft.PowerShell.Utility\Write-Error "Calculation timeout" return 0 } } Microsoft.PowerShell.Utility\Write-Verbose "Free fall completed in $time seconds" } end { # round the result to 2 decimal places for readability return [Math]::Round($time, 2d) } } |