Question

Suppose that after you are loaded into a Ferris wheel car, the wheel begins turning at 3 revolutions per second. The wheel has diameter 14 meters and the bottom seat of the wheel is 1 meter above the ground. Express the height h of the seat above the ground as a function of time t seconds after it begins turning.

Answer 1

since cos(t) starts at the top, and we are starting at the bottom (I assume, though it is not explicitly indicated),

h(t) = -cos(kt)

the wheel's radius is 7, and the center is 8m up, so

h(t) = 8-7cos(kt)

The period is 1/3, so 2π/k = 1/3, and k=6π

h(t) = 8-7cos(6πt)