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

Answer:

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

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

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

Answer 2

Answer:

$y = 2 + \frac{35}{2}(1 - cos(\frac{\pi}{3} t))$

Explanation:

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

$T = 6 min$

so we have

$\omega = \frac{2\pi}{T}$

$\omega = \frac{2\pi}{6} rad/min$

$\omega = \frac{\pi}{3} rad/min$

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

$\theta = \omega t$

so the height as a function of time is given as

$y = h_i + R - Rcos\theta$

$y = 2 + \frac{35}{2}(1 - cos(\frac{\pi}{3} t))$