How Does Incline Angle Affect Launch Speed in a Spring-Powered Pinball Machine?

[dareupgang]

Homework Statement

The ball launcher in a pinball machine has a spring that
has a force constant of 1.20 N/cm The surface
on which the ball moves is inclined 10.0° with respect
to the horizontal. If the spring is initially compressed
5.00 cm, find the launching speed of a 100-g ball when the
plunger is released. Friction and the mass of the plunger negligible

Homework Equations

Ki + Ws + Wg = Kf

The Attempt at a Solution

W = integral kx
but i don't understand where gravity comes into play. I'm trying to understand the concept, the solution manual works it out as 1.68 m/s and they use cos 100 don't understand that either

 

[Jolb]

I would do this problem by using conservation of energy. The energy in a spring is given by E = (1/2)kx^2, so plugging in your spring constant and initial compression gives you the initial energy, Ei.

Now all that energy goes into the pinball. The energy of the pinball is given by E = (1/2)mv^2 + mgh, where h is altitude. (There's where the gravitational acceleration comes into play). That's the final energy, Ef. Just equate Ei and Ef and then solve for v. h will represent the difference in altitude between the compressed position and the equillibrium position--so h=5cos(10°).