--[[ references ]]--
 
-- The code in this listing was derived from this first URL:
-- http://hyperphysics.phy-astr.gsu.edu/hbase/traj.html
-- http://en.wikipedia.org/wiki/Trajectory_of_a_projectile
 
 
--[[ support functions ]]--
 
function vxf(v, a)
        return v * math.cos(a * math.pi / 180)
end
 
function vyt(v, a, t)
        return v * math.sin(a * math.pi / 180) - 9.8 * t
end
 
function yt(v, a, t)
        return v * math.sin(a * math.pi / 180) * t - 0.5 * 9.8 * t * t
end
 
 
--[[ worker functions ]]--
 
function totalRangeHeightFlightTime(v, ag)
        local h = vyt(v, ag, 0) * vyt(v, ag, 0) / (2 * 9.8)
        local t = 2 * vyt(v, ag, 0) / 9.8
        local r = v * v * math.sin( 2 * ag * math.pi / 180 ) / 9.8
        return r, h, t
end
 
function positionAtTime(v, ag, t)
        local vx = vxf(v,ag) -- horizontal velocity
        local x = vxf(v,ag) * t -- horizontal distance
        local vy = vyt(v, ag, t) -- vertical velocity
        local y = yt(v, ag, t) -- height at time 't'
        
        return x, y, vx, vy
end
 
 
--[[ environment setup ]]--
 
local offsetX, offsetY = 50, 400
local iteration = 0.1
 
local v = 70 -- launch velocity v/ms
local ag = 80 -- launch angle (theta) degrees
local r, h, f = totalRangeHeightFlightTime(v, ag) -- total flight time
 
print( 'range: ', r )
print( 'height: ', h )
print( 'flight time: ', f )
 
 
--[[ trajectory plotting ]]--
 
for t=0, f, iteration do
        local x, y, vx, vy = positionAtTime(v, ag, t)
        print( math.round(x), math.round(y) )
        display.newCircle( x + offsetX, y * -1 + offsetY, (vx+vy)*.1 )
end