Kinetic Energy, Potential Energy, Work

[jskellington]

Hi! So this is a more general question about a question that I have already solved but I'm still confused and it seems like I'm missing the concept here.

Homework Statement

I'll try to recall the question as best I can from memory. A person is standing at a certain height h and shoots an object with some mass m at some angle z with a slingshot that acts as a spring with a k of k. The question asked for the velocity after the slingshot was released.

Homework Equations

Kf + Ugf = Ki + Ugi
1/2mvf^2 + mgy = 1/2mvi^2 + mgh
Ws = 1/2 kxi^2 + 1/2 kxf^2

The Attempt at a Solution

So basically what I did was plug in the values to find the work of the spring on the ball which I found to be 1/2kd^2. My main question is whether or not it is correct to substitute this value into the first equation above for Ki, the initial kinetic energy. This provided the correct answer and I found velocity by solving for Vf. I'm not sure if this makes any sense because I'm pretty confused myself. Thanks for any assistance.

 

[Delphi51]

Wouldn't it be easier to just use
spring energy -> kinetic energy
.5kx^2 = .5mv^2

 

[jskellington]

I suppose it would be--I think I've come up with my actual question now. When is it correct to substitute Work for Kinetic energy. Should I always substitute it in for Ki in the first equation and if it is vertical displacement, simply add mgh?

 

[Delphi51]

Sounds okay. I personally wouldn't bother with a W at all.
I think in terms of energy before = energy after
and put in whatever kinds of energy there are in each case.