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Rainy_Pass

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## Homework Statement

A 1000 kg roller coaster begins on a 10 m tall hill with an initial velocity of 6m/s and travels down before traveling up a second hill. As the coaster moves from its initial height to its lowest position, 1700J of energy is transformed to thermal energy by friction. In order for the roller coaster to safely travel over the second hill, it must be moving at a velocity of 4.6m/s or less at the top of the second hill. What is the maximum height the second hill can be?

## Homework Equations

KE = .5mv

^{2}

GPE = mgh

total energy = PE + KE + Th

_{e}

## The Attempt at a Solution

PE

_{max}= Total energy

PE = 1000kg (9.8 m/s

^{2}) 10m = 98,000J

KE = .5 (1000 kg) 4.6

^{2}= 10,580 J

Energy left at the bottom of the roller coaster = 98,000J - 1,700 J = 96,300 J

96, 300 J - 10,580 J = 85,720J

85,720 J = 1000kg (9.8 m/s

^{2}) h

h = 8.75m