.net - Compute trajectory using unit of measure -

i learning f# , trying use first time concept of unit of measure. have following questions:

• the last let (variable y in getposition function gives me following error: "the unit of measure ''u ^ 2 m/second' not match unit of measure 'm'". there wrong in formula or usage os unit of measure?

• i using unit of measures defined in microsoft.fsharp.data.unitsystems.si. there way not specify use shorter version of name? (e.g. unitnames.second vs second).

• i have use function cos , sin. these 2 functions expect float, not float. use languageprimitives.floatwithmeasure convert float unit of measure. way that? makes code verbose.

thanks!

open system open microsoft.fsharp.data.unitsystems.si  module generalballistictrajectory =      [<measure>] type radian      let gravitationalacceleration : float<unitnames.metre/unitnames.second^2> = 9.80665<unitnames.metre/unitnames.second^2>      let getposition (angle: float<radian>) (velocity: float<unitnames.metre/unitnames.second>)  (t: float<unitnames.second>) =         let x = velocity * t * (cos (float angle) |> languageprimitives.floatwithmeasure<unitnames.metre/unitnames.second>)         let abc = (0.5 * gravitationalacceleration) * t * t // returns float<unitnames.metre>          // unit of measure 'unitnames.metre' not match unit of measure 'unitnames.metre ^ 2/unitnames.second'         let y = (velocity * t * (sin (float angle) |> languageprimitives.floatwithmeasure<unitnames.metre/unitnames.second>)) - abc          (x, y) 

you can use shorter names adding

open microsoft.fsharp.data.unitsystems.si.unitnames 

to file.

as error, it's not clear why converting result of sin call measure type, since velocity * t has same measure type (meter) abc. following appears want:

open system open microsoft.fsharp.data.unitsystems.si open microsoft.fsharp.data.unitsystems.si.unitnames  module generalballistictrajectory =      [<measure>] type radian      let gravitationalacceleration : float<metre/second^2> = 9.80665<metre/second^2>      let getposition (angle: float<radian>) (velocity: float<metre/second>)  (t: float<second>) =         let x = velocity * t * (cos (float angle) |> languageprimitives.floatwithmeasure<metre/second>)         let abc = (0.5 * gravitationalacceleration) * t * t // returns float<unitnames.metre>          let y = (velocity * t * (sin (float angle))) - abc         (x, y)