Question

At the amusement park, you decide to ride the Ferris wheel, which has a maximum height of 50 meters and a diameter of 35 meters. It takes the wheel 13 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)=13sin(2pi/35 t)+50. is this correct?

Answer 1

diameter is 35, so radius is 17.5 -- that is the amplitude of f(t)

f(t) is like 17.5 sin(t)

Since the max height is 50, that means the axle is at 50-17.5 = 32.5

f(t) is like 17.5 sin(t) + 32.5

The period of sin(kt) is 2pi/k, so we need

2pi/k = 13
k = 2pi/13

f(t) = 17.5 sin(2pi/13 t) + 32.5

where t is in minutes since boarding.

That function means that you board the wheel at axle height. If you board at the bottom of the rotation, then you have

f(t) = 32.5 - 17.5 cos(2pi/13 t)

That means that you board from a platform 15 feet off the ground.

You really got your constants all mixed up...