Well, the catapult capx is pretty explanatory.
The three states of the button mouse are the same that in the touch object.
(On touch start, is touching object, on touch end)
On touch start, you display the arm, the trajectory (as a sprite, like greenarrow is in catapult) and the gift.
Is touching object, you set the angle of your arm and of your direction.
On touch end, you apply a force on your gift.
You can read more about the force and such in the physic tutorials (basic and advanced)