i think the common approach would be to give the “bird” an impulse with a specific force and direction, e.g. depending on the mouse position relative to the slingshot when you drag the “bird” to fire it. (http://v-play.net/doc/vplay1-colliderbase.html#applyLinearImpulse-method) This method is used in VPong and VZombieBreak if you need any demo source code.
Regarding the trajectory, there is no predefined solution for this, but similar questions have been asked in the web several times. Searching for “arcpath angry birds” or something like that should hopefully give you some ideas on how to solve this problem.