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Roller-coaster car speed using energy conservation. Assuming the height of the hill in Fig. 6-18...

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Roller-coaster car speed using energy conservation. Assuming the height of the hill in Fig. 6-18 is 40 m, and the roller-coaster car starts from rest at the top, calculate (a) the speed of the roller-coaster car at the bottom of the hill, and (b) at what height it will have half this speed. Take y = 0 at the bottom of the hill. APPROACH We use conservation of mechanical energy. We choose point 1 to be where the car starts from rest (v? = 0) at the top of the hill (y? = 40 m). In part (a), point 2 is the bottom of the hill, which we choose as our reference level, so y? = 0. In part (b) we let y? be the unknown.

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