Is a 15.0-g Ball from a Spring Gun Safe Without Goggles for Children?

[knowNothing23]

Homework Statement

Conservation of energy
You are designing a game for small children and want to see if the
ball’s maximum speed is sufficient to require the use of goggles. In your game, a
15.0-g ball is to be shot from a spring gun whose spring has a force constant of
600 N/m. The spring will be compressed 5.00 cm when in use. How fast will the
ball be moving as it leaves the gun and how high will the ball go if the gun is
aimed vertically upward? What would be your recommendation on the use of
goggles?

I have set the gravitational potential energy zero at the mouth of the gun; therefore, the initial gravitational potential energy is negative.

Could anyone help?
Thank you.

Homework Equations

The Attempt at a Solution

My velocity's answer is different than the one from the book.

Wext = ΔK + ΔU g + ΔU s = 0
or, because Ki = Us,f = Ug,f = 0, **"f" as in final**

(1/2)m(vf)^(2) - mgx − (1/2)k (x)^(2) = 0

 

[Doc Al]

I have set the gravitational potential energy zero at the mouth of the gun; therefore, the initial gravitational potential energy is negative.

OK, but what's the change in gravitational PE?

 

[knowNothing23]

-+-= +.

Thank you.