Question

A power outage occurs 6 min after the ride started passengers must wait for their cage to be manually cranked into the lowest position in order to exit the ride. Sine function model: 82.5 sin 3 pi (t+0.5)+97.5 where h is the height of the last passenger above ground measured in feet t is the time of operation of the ride. The complete ride takes 15 minutes.

(A)- What is the height of the last passenger at the moment of the power outage?
(B)- will the last passenger to board the ride need to wait to exit the ride?

Answer 1

h = 15 ft

He would not have to wait - Already at the bottom!

Explanation:

Given:-

- The position of the last passenger from ground on the ferris wheel is given by a sine function as follows:

h = 82.5*sin(3*pi*(t + 0.5)) + 97.5

- The ride takes 15 minutes to complete.

- The power outage occurs at 6 mins.

Find:-

(A)- What is the height of the last passenger at the moment of the power outage?

(B)- will the last passenger to board the ride need to wait to exit the ride?

Solution:-

- The height of the last passenger at t = 6 mins from start point can be evaluated from the given modelling function h.

h = 82.5*sin(3*pi*(6 + 0.5)) + 97.5

h = 82.5*(-1) + 97.5

h = 15 ft

- How far away is the last passenger at t = 6 mins from bottom position for him to exit the ride.

Min [h] = [ 82.5*sin(3*pi*(t + 0.5)) + 97.5 ]

Min [sin ( at + b ) ] = -1

Min [h] = 82.5(-1) + 97.5

= 15 ft

- After 6 mins the last passenger is already at the bottom most position. He would not have to wait!