Question

a ferris wheel is 50 meters in diameter and boarded from a platform that is 4 meters above the ground. the six oclock position on the ferris wheel is level with the loading platform. the wheel completes 1 full revolution in 4 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 2 minutes?
meters

Explanation:

Step1: Find Amplitude

Amplitude of a Ferris wheel is half its diameter. The diameter is 50 meters, so amplitude \( A=\frac{50}{2}=25 \) meters.

Step2: Find Midline

Midline is the average of the maximum and minimum heights. The minimum height is 4 meters (platform height, since 6 o'clock is at platform level). The maximum height is platform height + diameter = \( 4 + 50 = 54 \) meters. Midline \( y=\frac{4 + 54}{2}=\frac{58}{2}=29 \) meters.

Step3: Find Period

The wheel completes 1 full revolution in 4 minutes, so the period \( T = 4 \) minutes.

Step4: Height after 2 minutes

After 2 minutes, the wheel has completed half a revolution (since period is 4 minutes). Starting at 6 o'clock (level with platform, 4 meters), after half a revolution, we are at 12 o'clock, which is maximum height. Maximum height is \( 4 + 50 = 54 \) meters.

Answer:

Amplitude: \( \boldsymbol{25} \) meters
Midline: \( y = \boldsymbol{29} \) meters
Period: \( \boldsymbol{4} \) minutes
Height after 2 minutes: \( \boldsymbol{54} \) meters