SOLUTION: The height,h, in meters, above the ground of a cart as a ferris wheel rotates can be modelled by the function h(t) = -15cos(πt/45) +16 where t is the time in seconds. A.) Find t

Algebra ->  Trigonometry-basics -> SOLUTION: The height,h, in meters, above the ground of a cart as a ferris wheel rotates can be modelled by the function h(t) = -15cos(πt/45) +16 where t is the time in seconds. A.) Find t      Log On


   

Question 1204545: The height,h, in meters, above the ground of a cart as a ferris wheel rotates can be modelled by the function h(t) = -15cos(πt/45) +16 where t is the time in seconds.
A.) Find the radius of the ferris wheel
B.) How long does it take to revolve once ?
C.) At what height does the cart start at?
Answer by math_tutor2020(3817) About Me  (Show Source):
You can put this solution on YOUR website!

Answers:
  1. 15 meters
  2. 90 seconds
  3. 1 meter
Explanation for part (a)
The radius of the wheel is equal to the amplitude.
The template y+=+A%2Acos%28B%28x-C%29%29%2BD has |A| as the amplitude.
In this case the amplitude is |-15| = 15.


An alternative approach for part (a)
The highest and lowest points are when h(t) = 31 meters and h(t) = 1 meter respectively (recall that -1+%3C=+cos%28x%29+%3C=+1).
This is a distance of 31-1 = 30 meters, which represents the diameter of the wheel. The radius is half that.


Explanation for part (b)
The period T is calculated with the formula T+=+%282pi%29%2F%28B%29.
In this case B+=+pi%2F45.
Plug that value of B into the equation to get T = 90. The cosine curve repeats itself every 90 seconds.


Explanation for part (c)
Plug in t = 0 to get h(0) = 1.
I'll leave the scratch work and steps for the student to do.