question 3 a ferris wheel is 25 meters in diameter and boarded from a platform that is 3 meters above the…

Explanation:

Step1: Find the amplitude

The amplitude of a sinusoidal - like function for a Ferris - wheel problem is half of the diameter. Given the diameter $d = 25$ meters, so the amplitude $A=\frac{d}{2}$. $A=\frac{25}{2}=12.5$

Step2: Find the mid - line

The mid - line is the average of the maximum and minimum heights. The minimum height is the height of the platform, which is $h_{min}=3$ meters, and the maximum height is $h_{max}=3 + 25=28$ meters. The mid - line $y=\frac{h_{min}+h_{max}}{2}=\frac{3 + 28}{2}=\frac{31}{2}=15.5$ meters.

Step3: Find the period

The period is the time it takes for the Ferris wheel to complete one full revolution. Given that the wheel completes 1 full revolution in 10 minutes, so the period $T = 10$ minutes.

Step4: Find the height at $t = 5$ minutes

Since the period $T = 10$ minutes, at $t = 5$ minutes, the Ferris wheel has completed half a revolution. If it starts at the six - o'clock position (level with the loading platform at $h = 3$ meters), after half a revolution, it will be at the twelve - o'clock position. The height at the twelve - o'clock position is $h=3 + 25=28$ meters.

Answer:

Amplitude: 12.5 meters Midline: $y = 15.5$ meters Period: 10 minutes Height at 5 minutes: 28 meters