Determine the required height h of the roller coaster so that when it is essentially at rest at the crest of the hill it will reach a speed v when it comes to the bottom. Also, what should be the minimum radius of curvature ρ for the track at B so that the passengers do not experience a normal force greater than kmg? Neglect the size of the car and passengers.

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Given: v = 100 k = 4 Solution: T1 + U12 = T2 1 2 2 m² mgh = km hr h = 2 1 v² V 2 g h = 39.3 m