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## Homework Statement

A roller coaster at an amusement park is at rest on top of a 30 m hill (point A). The car starts to roll down the hill and reaches point B which is 10 m above the ground, and then rolls up the track to point C, which is 20 m above the ground.

(A) A student assumes no energy is lost, and solves for how fast the car is moving at point C using energy arguments. What answer does he get?

(B) If the final speed at C is actually measured to be 2 m/s, what percentage of energy was "lost" and where did it go?

## Homework Equations

K

_{f}+ U

_{f}= K

_{i}+ U

_{f}

K = 1/2mv

^{2}

U

_{g}= mgh

## The Attempt at a Solution

I believe there is a typo in the book for Part A, I think they got the height wrong, their answer is 20 m/s. For Part B, I think I did something wrong because the height error has been corrected.

**My Work for Part A:**

I set potential energy at A equal to kinetic energy at C. My reference point is considering the height of C as ground level.

mgh = 1/2mv

^{2}

gh = 1/2v

^{2}

10*10 = 1/2v

^{2}

100 = 1/2v

^{2}

200 = v

^{2}

14 = v

**Their Work for Part A**

My Work for Part B

My Work for Part B

Find ratio of Final Energy to Initial Energy and subtract from 100%

[itex]\frac{\frac{1}{2}mv^2}{mgh}[/itex]

[itex]\frac{\frac{1}{2}v^2}{gh}[/itex]

[itex]\frac{\frac{1}{2}*2^2}{10*10}[/itex]

[itex]\frac{2}{100}[/itex]

2%

So 98% is lost to heat. This is radically different from their answer:

For this part I again used a reference height of the height at C, but am I not allowed to do that?

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