Question

50 POINTS PLEASE HELP!!!

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

after 2/3 min the height of the passengers would be the same

Explanation:

Answer 2

Period =
`(2)/(3)`

The ferris wheel will complete one round in 40 seconds.

Explanation:

We are given the function representing the height of the wheel by,

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

Now, we know that if a function f(x) has period P, then a×f(bx+c)+d will have the period
`(P)/(|b|)`.

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

Therefore, the period of this function is
`(2)/(3)`.

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

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