Using Hooke's law to find the pull back distance?

[grover1213]

Homework Statement

I'm given the mass of the object and acceleration (gravity), and I'm given the pull back distance of one test of the slingshot. I've found the k constant by finding force with f=ma, but I need to find the pull back distance using the same slingshot in order to propel the object a certain distance. My question is that because the distance seems to have no effect on the force, (because it is only mass times acceleration), if I solved for the pull back distance with the force, wouldn't I get the same pull back distance that i used with the first equation?

Homework Equations

F=-kx

The Attempt at a Solution

 

[PhanthomJay]

You will have to be more specific about the problem statement. Since F = kx, as you pull back the slingshot more, x increases, so therefore, F increases. And since F_net = ma, since F is now larger when you pull the slingshot back, then the object in the sling will accelerate more during its period of contact with the sling, until it leaves it. And since it accelerates more, then it's speed will be higher when it leaves the sling, and will travel a greater distance. hcceleration of the object in the slingshot is not the acceleration of gravity in either case.