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**1. 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.

**2. Homework Equations**

**3. 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