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?

My answers:

(A): 79 feet
(B) the last passenger will need to wait to exit the ride because they are 20-25ft above ground.

Answer 1

Oof I’m struggling with this too

Answer 2

I will assume
h = 82.5 sin (3 pi (t+0.5) )+97.5 , (you had no equation and no h)

so when t = 6
h = 82.5 sin (3π(6.5)) + 97.5
= 82.5(-1) + 97.5 = 15

check: period = 2π/(3π) = 2/3 minutes (that is a fast ride considering how huge it is)
So 6 ÷(2/3) = 9 , at the 6 minute mark, the last passenger has just completed 9 rotations.

the min height of the basket is -82.5 + 97.5 = 15
( the min value of 82.5 sin(anything) = 82.5(-1) )

so the last passenger must be at the platform level.

how did you get 79 ???