(a) A plane at velocity 100m/s in still air is flying from station P due North to station Q. A helicopter at velocity 50m/s in still air is flying from P due East to station C. If wind at velocity 20m/s blows due East when the plane and helicopter are flying, calculate the: (i) Resultant velocities of the plane and helicopter (ii) Velocity of th…

Plane vs Helicopter.fsx

[<Measure>]
type m

[<Measure>]
type s

type Vector<[<Measure>] 't> =
    { X: float<'t>; Y: float<'t> }

    with
        static member Zero : Vector<'t> = { X = 0.0<_>; Y = 0.0<_> }
        static member (+) (v1, v2) = { X = v1.X + v2.X; Y = v1.Y + v2.Y }
        member v.Length = sqrt (v.X * v.X + v.Y * v.Y)

let planeVelocity, helicopterVelocity, windVelocity =
        { Vector<m/s>.Zero with Y = 1e2<_> }
        , { Vector<_>.Zero with X = 5e1<m/s> }
        , { Vector<_>.Zero with X = 2e1<m/s> }

let planeResultant, helicopterResultant =
    planeVelocity + windVelocity
    , helicopterVelocity + windVelocity

let helicopterResultantRelativeToPlane = planeResultant + helicopterResultant

let planeAbsolute, heliAbsolute, relativeAbsolute =
    planeResultant.Length, helicopterResultant.Length, helicopterResultantRelativeToPlane.Length