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## Homework Statement

Suppose a car approaches a hill and has an initial speed of 116 km/h at the bottom of the hill. The driver takes her foot off of the gas pedal and allows the car to coast up the hill.

**Randomized Variables**

*vi*= 116 km/h

*m*= 780 kg

*h*= 20.5 m

*a*= 2.3 °

**Part (a)**If the car has the initial speed stated at a height of h = 0, how high (in m) can the car coast up a hill if work done by friction is negligible?

**Part (b)**If, in actuality, a 780-kg car with an initial speed of 116 km/h is observed to coast up a hill and stops at a height 20.5 m above its starting point, how much thermal energy was generated by friction in J?

## Homework Equations

U2 + K2 = U1 + K1 + W_other

U2 is final potential energy.

K2 is final kinetic energy.

## The Attempt at a Solution

Part (a) I got right.

1/2(mv^2) + mgh = 0

h = v^2/(2g)

=(32.2 m/s)^2 /(2*9.8m/s^2) = 52.9m

Part (b) I need help. (FK stands for friction force and s stands for displacement.)

I tried U2 + 0 = U1 + K1 + W_other.

W_other = -FK*s = U2 - U1 - K1

-FK*s = mg(Y2 - Y1) - 1/2(m*v^2)

-FK*s = 780kg*9.8m/s^2(20.5m*sin(2.3) - 52.9m) - 1/2(780kg*(32.2m/s)^2)

-FK*s = -652033j

FK = -(-652033j) / s

FK = 652033 j / (20.5m - 52.9m)

FK = -20124 N

The correct answer is 248200 j