A wooden roller coaster contains a run in the shape of a sinusoidal curve, with a series of hills. The crest of each hill is 10
8 feet above the ground. If it takes a car 1.9 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(ωt - Φ) + B that models the motion of the coaster train during this run starting at the top of a hill.
We have to find a sinusoidal function of the form y = A sin(ωt - Φ) + B that models the motion of the coaster train during this run starting at the top of a hill.
We are given
Amplitude,
Using the formula
We assume,
Horizontal shift
Substitute the values
Hence, the sinusoidal function that models the motion of the coaster train during this run starting at the top of a hill is given by