Question

20 POINTS!

The Colossus Ferris wheel debuted at the 1984 New Orleans World’s Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min ride.

Answer 1

Period =
`(2)/(3)`

The Ferris wheel will complete one round in 40 seconds.

Explanation:

We have the function representing the height of the passenger by,

`h=82.5 \sin 3\pi(t+0.5)+97.5`, where t = time in minutes.

It is known that when a function f(x) has period P, then the function a×f(bx+c)+d will have the period
`(P)/(|b|)`.

Since, the function
`\sin x` has period
`2\pi`, so the function h will have period
`(2\pi)/(3\pi)` i.e.
`(2)/(3)`.

Thus, the period of the given function is
`(2)/(3)`.

Now, as the period is
`(2)/(3)` minutes i.e 40 seconds.

Hence, we get that the Ferris wheel will complete one round in 40 seconds.