4 . A child of mass m = 24 kg slides down a slide of height h = 2.5 m without friction. Let gravitational potential energy be zero at ground level.

Part (a) tell an

expression for the child's total mechanical energy, E, at the top of the slide, in terms of the variables in the problem and the acceleration due to gravity g.

Part (b) Calculate the change in the child's potential energy, AU in joules, from the top to the bottom of the slide at

ground level (i.e. AU = Uground - Utop).

Part (c) What is the child's final speed, vf in m/s?

5 . A roller coaster car has a speed of vp = 6.9 m/s as it tops the crest of a h = 27.5 m drop. What is the car's speed at the bottom of the drop, vf in m/s?

6 . 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.

Part (a) If the car has the initial speed stated at a height of h = 0, how high, in meters, can the car coast up a hill if work

done by friction is negligible?

Part (b) If, in actuality, a 720-kg car with an initial speed of 116 km/h is observed to coast up a hill and stops at a height 23.5 m above its starting point, how much thermal energy was generated by friction in J?

Part (c) What is the magnitude of the average force of friction, in newtons, if the hill has a slope 2.6 above the horizontal?