Question

A ferris wheel is 15 meters in diameter and boarded from a platform that is 4 meters above the ground. The six o'clock position on the ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 2 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. Write an equation for h = f(t).

Answer 1

The equation for h = f(t) will be, ⁣$\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5$.

What is a function?

A connection between independent variables and the dependent variable is defined by the function. Functions help to represent graphs and equations.

The given data in the problem is;

Ferris wheel diameter,d= 15 meters

The platform is 5 m above the ground.

The Ferris wheel function is;

h(t) = A sin(Bt + C) + D

Here,

A is Amplitude

D is the midline

B is period

C is a phase shift

t is the time

The amplitude of the function is half of the diameter;

A = d/2

A=15 m /2

A = 7.5 m

The value of the mid-line is found as;

Mid-line =  amplitude  + distance from the mid-line;

D= 7.5 + 5

D = 12.5

From the given data, the wheel completes 1 full revolution in 2 minutes

The period of the wheel is T.

B = 2

The phase shift is found as;

$\rm \frac{C}{\pi}=\frac{-1}{2}\\\\ {C}=\frac{-\pi}{2}$

The Ferris wheel function is;

h(t) = A sin(Bt + C) + D

Substitute the obtained values we get;

$\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5$

Hence, the equation for h = f(t) will be, ⁣$\rm h(t)=7.5sin({\pi}t-\frac{\pi}{2})+12.5$.

To learn more about the function, refer to the link brainly.com/question/12431044.

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