Chapter 6.6, Problem 35AYU

Challenge Problem Coaster Motion A wooden roller snider at Six Flags contains a run in the shape of a sinusoidal curve, with a series of hills. The crest of each hill is $106$ feet above the ground. If it takes a car $1.8$ seconds to go from the top of a hill to the bottom ( $4$ feet off the ground), find a sinusoidal function of the form

$y=A\sin \left(\omega \chi -\varphi \right)+B$

that models the motion of the coaster train dining this run starting at the top of a hill.