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## Homework Statement

Assume no friction. A 58-kg teenager at a water park slides down a long, winding waterslide of varying slope. The slide has a net height difference of 30. m from start to finish, and the teenager starts from rest. Throughout the problem, let y=0 and Ugrav = 0 at the end (bottom) of the slide.

a) What is the teenager's net loss of gravitation potential energy?

b) If the slide is frictionless, what is the teenager's net gain of kinetic energy?

c) What is the teenager's total mechanical energy?

## Homework Equations

I know that

W = Kf - Ko + Uf - Uo

## The Attempt at a Solution

Since there is no friction, W = 0

And since Ugrav = 0, Uf and Ko cancels out

this gives me Kf = Uo (KE gained is PE lost)

=> (1/2) *m*v^2 = mgh

After calculating for Uo, I get (58 kg) * (9.8 m/s^2) * (30. m) = 17040 J = 17.04 kj

My given choices are

A. -490 J D. -6.8 kJ

B. -860 J E. -12 kJ

C. -2.9 kJ F. -17 kJ

My guess is that for a, Uo = -17 kj (negative since it's lost) & for part b, Kf = 17 kJ (positive since it's gained). Is that right?

But I need help in doing part C also. Is mechanical energy the sum of both Uo and Kf?

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