What effects the displacement of object from a slingshot

[naomi newhouse]

hey,
What would be the things that effect the displacement of an object when fired from a slingshot?
I assume that is would be mass, distance the rubber is pulled back, the speed of release for the rubber and the angle. But in what was would they effect the displacement.

What are the formulas that i could use to figure these things out?

 

[andrewkirk]

First you need the spring constant of the elastic, the mass of the object and the distance the object is pulled back before release. Hooke's law and Newton's law of F=ma will give you the acceleration of the object in terms of the distance from the centre of the slingshot after release, which is a simple differential equation. Solving that will give you the velocity when the object passes that centre point.

From there you just use Newton's laws of linear motion, given that release velocity and additional inputs of the angle of the slingshot from horizontal and its height above the ground. One would usually assume the ground is level and ignore air resistance.