Question

A Ferris wheel has a radius of 28 feet and completes 3 revolution in 1.5 minutes. Assume the rider begins at the lowest point of the wheel, 2 feet above ground level. Model the height of the rider, in feet above the ground, as a function of time in seconds, using a sine equation with only positive numbers in the final equation.

Answer 1

Step-by-step explanation

We have that the radius of a Ferris wheel is 28 feet.

Because the wheel is rotating, the radius represents the amplitude of the rotation, that is the highest vertical distance from the centre of the wheel.

Therefore:

A = 28 feet

The wheel completes 3 revolutions in 1.5 minutes (90 seconds).

The period is the time it takes to complete one revolution. So, we have that:

`P\text{ = }(90)/(3)\text{ = 30 seconds}`

Since the rider begins 2 feet above the ground (lowest point of the wheel), we can say that the vertical shift is 2 feet.

The general form of a since function is given as:

`y\text{ = A\lbrack{}sin}(2\pi)/(P)(x\text{ - C)\rbrack + D}`

where A = amplitude

B = 2π/P

C = horizontal shift

D = vertical shift

Therefore, the sine function representing the height of the Ferris wheel is: