LÖVE

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local x = self.target.x - self.position.x
local y = self.target.y - self.position.y

res.body:applyLinearImpulse(x * 10 ^ 10, y * 10 ^ 10)

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function Catapult:pushRock()
    local pos = getDrawPosition(self)
    --rock spawn position
    pos.x = pos.x + 3
    pos.y = pos.y - 3
    
    --distance on both axises
    local x = self.target.x - pos.x
    local y = self.target.y - pos.y
    
    local _, g = world:getGravity() --world:getGravity() returns gravity.x and gravity.y; gravity.x = 0
    
    local t = 6                    --time. Can be any, except zero
    local vx = x / t                --velocity on X
    local vy = y / t - g * t / 2    --velocity on Y
    
    Rock:new(pos.x, pos.y, vx + math.random(4) - 2, vy - math.random(4) + 2)
end

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-- STEP ONE: figure out the velocity required to reach the target
-- vector to target:
local dx = self.target.x - self.position.x
local dy = self.target.y - self.position.y
-- distance to target:
local d = math.sqrt(dx*dx + dy*dy)
assert(d > 0, "target == position")
-- normalized vector to target:
local nx = dx/d
local ny = dy/d
-- velocity required to reach the target:
local vx = nx*desiredLV
local vy = ny*desiredLV
-- minimum time to reach the target:
local dt = d/desiredLV

-- STEP TWO: factor in gravity and linear damping
-- adjust the velocity to compensate for the effects of gravity and linear damping:
-- v = v - g
vx, vy = steering.compG(vx, vy, gx, gy, dt) -- ignore if "gx" and "gy" are 0
vx, vy = steering.compLD(vx, vy, damping, maxLV, dt) -- ignore if "damping" is 0 

-- STEP THREE: find the force based on the velocity: F = m*a, a = (fv - iv)/dt, dt = d/desiredLV
-- initial velocity, in this case 0, 0:
local ivx, ivy = 0, 0 -- body:GetLinearVelocity()
-- final velocity:
local fvx, fvy = vx, vy
-- force required to reach the final velocity:
local fx, fy = steering.force(ivx, ivy, fvx, fvy, mass, dt)

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gx, gy: world gravity
damping: linear damping of the body
mass: mass of the body
maxLV: maximum linear velocity (Box2D constant)
desiredLV: desired linear velocity (0 < desired LV <= maxLV)
dt: time interval (> 0) in this case: dt = d/desiredLV