A circular ferris wheel is 44 meters in diameter. Ash and Jess enter a carriage at the bottom of the wheel and get off 18 minutes later after going around 6 times.

Question

When a carriage is at the bottom of the wheel, it is 1 meter off the ground

Questions:

Determine the period of the function and interpret what this value represents in the context of the question.

Write the equation of the function h(t) that models the height of the carriage Ash and Jess rode in, t minutes after the ferris wheel started moving.

Sketch h(t) on a graph over the domain 0<t<6

Someone please help this question is so hard and I can’t find anything on the internet that’ll help.

Answer 1

Hello Jenna,

You can pause the video to look at the details. Feel free to comment with a followup question.

Answer 2

a) The period of a function is the value p such that f(x) = f(x + p). In this case, the period is the amount of time the ferris wheel takes to complete a full rotation. Since they go around the ferris wheel 6 times in 18 minutes, it takes them 3 minutes to complete a full rotation, and the period is 3 minutes.

b) h(t) is the vertical motion as the circle rotates, which is represented by:

h(t) = a sin (bt) + c

where a is the radius of the circle, 2π/b is the period of the function, and c is the vertical translation. We know that the period is 3 minutes, the radius is 22m, and the center of the carriage is 22 + 1 = 23m off the ground. We also start from the bottom of the wheel, which represents a 90 degree translation of the function. Therefore, we have:

h(t) = 22sin(2πt/3 - π/2) + 23

c) Can't draw it here, but draw a sine wave with an amplitude of 22, a midline at y = 23, starts the period at π/2, and ends the period 3 min later.