At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 80 meters and a diameter of 40 meters. It takes the wheel seven minutes to make one revolution. Write the sinusoidal function, f(t), that models the height of your chair at any time, t.

Question

At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 80 meters and a diameter of 40 meters. It takes the wheel seven minutes to make one revolution. Write the sinusoidal function, f(t), that models the height of your chair at any time, t.
I got f(t)=20sin(2pi/7)t+40. Is this correct?

Anonymous · Answer

Your 2pi/7 t is correct.

To get the max height of 80 with a radius of 20, you need

20sin(2pi/7t)+60

It could also be a cosine function, or either sine or cosine with a phase shift. Your pure sine function indicates that at t=0, the chair is level with the axle of the wheel.