Question

A Ferris wheel has a diameter of 20 feet and the bottom of the wheel is 5 feet off of the ground. The rider starts at the bottom of the ride and it takes 3 minutes to complete one revolution. Find and sketch a sinusoidal model that could be used to estimate the nder's height throughout the ride and then use the model to calculate the rider's height after 2 minutes Model:________ Height after 2 min:________

Answer 1

Height = 15 + 10sin((2pi/3)t)

`\text{Height = 15 + 10 }\cdot\text{ sin(}(2\pi)/(3)t)`

Where t is time in minutes

15 ==> height of the center of the wheel (5 feet off the ground plus 10 feet radius of the wheel)

10 ==> radius of the wheel

angular velocity = 2pi/3 radians per minute

Height after 2 min: 6.34 feet

`H\text{ = 15 + 10 }\cdot\text{ sin(}(2\pi)/(3)2)\text{ =15 + 10 }\cdot\text{ }(-0.866)\text{ = }15\text{ - }8.66\text{ = }6.34`