A Ferris Wheel has a radius of 22 meters and can make a revolution in 82 seconds. Passengers board at the bottom, at a height of 3 m.

Write a sinusoidal equation that models a rider's height as a function of time (Use h(t) and t as your dependent and independent variables, respectively.)

radius of 22

h = 22 sin t
revolution in 82 seconds
h = 22 sin(2π/82 t)
board at the bottom: use -cos instead of sine
board at h=3
h = 25 - 22 cos(2π/82 t)

During the first two rotations, at what time and height does the instantaneous rate of change does ''h = 25 - 22 cos(2π/82 t)'' have the greatest positive value?

To model a rider's height as a function of time on the Ferris Wheel, we can use a sinusoidal equation. The general form of a sinusoidal equation is given by:

h(t) = A sin(B(t - C)) + D

Where:
A represents the amplitude of the function, which is the maximum distance from the average height.
B represents the period, which is the time it takes to complete one full cycle or revolution.
C represents the phase shift, which indicates any horizontal shift in the function.
D represents the vertical shift, which indicates any vertical shift in the function.

In this case, the Ferris Wheel has a radius of 22 meters, which means the amplitude is 22. The period is given as 82 seconds, so B can be calculated as 2π divided by the period (B = 2π / 82). The phase shift is 0 in this case since passengers board at the bottom. Finally, the vertical shift is 3 meters, as passengers board at a height of 3 meters.

Putting it all together, the equation that models a rider's height as a function of time on the Ferris Wheel is:

h(t) = 22 sin((2π / 82)(t - 0)) + 3