Physics Homework MKII

local tArgs = {...}
VelocityInitial = 8.9

function GetHoopHeight(theta, Vi)

    --set initial values
    Vi = Vi or VelocityInitial
    theta = math.rad(theta)
    Viy = Vi*math.sin(theta)
    Vix = Vi*math.cos(theta)

    --figure out how much time it will take the ball to move 4 meters
    airTime = 4/Vix

    --figure out how high the ball will be at this time
    deltaY = Viy*airTime + -4.905*airTime^2 + 1

    --return answer
    return deltaY
end

function GetBucketDistance(theta, Vi)

    --set initial values
    Vi = Vi or VelocityInitial
    theta = math.rad(theta)
    Viy = Vi*math.sin(theta)
    Vix = Vi*math.cos(theta)

    --use the quadratic formula to figure out the function zeros for time in air
    quad1 = (-Viy + math.sqrt(Viy^2 + 19.62))/-9.81
    quad2 = (-Viy - math.sqrt(Viy^2 + 19.62))/-9.81

    --discern which zero is relevant (only one is positive, that's the one required)
    airTime = math.max(quad1, quad2)

    --figure out how far the ball will go before hitting the ground
    deltaX = Vix*airTime

    --return answer
    return deltaX
end

hoop = GetHoopHeight(tArgs[1], tArgs[2])
bucket = GetBucketDistance(tArgs[1], tArgs[2])
print("Hoop Height: " .. hoop)
print("Bucket Distance: " .. bucket)