Predictions?

#!/usr/bin/env lua

local g = 9.81 -- fixme

local function angle_to_impact(vel, dist, heightdiff)
    local v2 = math.pow(vel, 2)
    local v4 = math.pow(vel, 4)

    local sq = math.sqrt(math.abs(v4 - (g * (g*dist*dist + 2 * heightdiff * v2))))

    local top = 0
    if v2 - sq < 0 then
        top = v2 + sq
    else
        top = v2 - sq
    end

    local bot = g * dist

    return math.atan(top / bot) / math.pi * 180
end

local function time_to_impact(vel, dist)
    local v2 = math.pow(vel, 2)
    local v4 = math.pow(vel, 4)

    local minus = v2 - math.sqrt(vel - 4 * v4 * dist)
    local plus = v2 + math.sqrt(vel - 4 * v4 * dist)

    local res

    if minus < 0 then
        res = math.sqrt(plus / (2 * v2))
    else
        res = math.sqrt(minus/ (2 * v2))
    end

    return res
end


print "distance = 100m"
print("v0 = 25m/s, ", angle_to_impact(25, 100, 0))
print("v0 = 50m/s, ", angle_to_impact(50, 100, 0))
print("v0 = 75m/s, ", angle_to_impact(75, 100, 0))

--kobra@pc:~/Desktop$ ./projectiles.lua
--distance = 100m
--v0 = 25m,     54.614324981375
--v0 = 50m,     11.551958535305
--v0 = 75m,     5.0218718579104