Question

A ferris wheel is 35 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 6 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

Answer 1

`y = 2 + (35)/(2)(1 - cos((\pi)/(3) t))`

Step-by-step explanation:

As we know that time period of the ferris wheel is given as

`T = 6 min`

so we have

`\omega = (2\pi)/(T)`

`\omega = (2\pi)/(6) rad/min`

`\omega = (\pi)/(3) rad/min`

now angular position at any time "t" is given as

`\theta = \omega t`

so the height as a function of time is given as

`y = h_i + R - Rcos\theta`

`y = 2 + (35)/(2)(1 - cos((\pi)/(3) t))`

Answer 2

`h=f(t)= -17.5cos(\pi /3)+20.5`

Step-by-step explanation:

Amplitude is 35/2=17.5

Midline= Distance from ground + Amplitude = 17.5+3= 20.5

Period is time taken to finish 6 minutes

2π/b=T

2π/b=6

b=π/3

`h=f(t)= -17.5cos(\pi /3)+20.5`