Question

A ferris wheel is 45 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 10 minutes. The function h = f(t) gives your height in meters above the ground t minutes after the wheel begins to turn. What is the Amplitude? meters What is the Midline? y = meters What is the Period? minutes How High are you off of the ground after 4 minutes? meters

Answer 1

If the wheel rotates clockwise, the height function is h(t) = 28.5 + 22.5sin(270 - 36t).

The function's central axis for the height of the Ferris wheel's center is given by h = f(t).

= 6 + 45 ÷ 2 = 6 + 22.5 = 28.5 meters.

The wheel rotates at a speed of 36 degrees per minute since the period of revolution is 10 minutes.

The wheel's direction of rotation—clockwise or counterclockwise—is not specified.

Let's look at both situations:

The present angle, assuming it spins clockwise, is equal to 270 – 36t degrees, where t is the duration in minutes.

Then the height function h = f(t)

= 28.5 + 22.5sin(a)

= 28.5 + 22.5sin(270 - 36t)

If the wheel rotates anti-clockwise, the current angle is

b = 270 + 36t degrees.

Then the height function

h = r(t)

= 28.5 + 22.5sin(b)

= 28.5 + 22.5sin(270 + 36t)

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