the graph shows a complete cycle of the sinusoidal function, representing the height of a ferris wheel with…

the graph shows a complete cycle of the sinusoidal function, representing the height of a ferris wheel with respect to time. a ferris wheel is 30 meters in diameter and is raised on a platform 8 feet from the ground so that the bottom of the wheel is in line with the top of the platform. a ride lasts 20 minutes and undergoes five revolutions in a clockwise direction during this time. if brad is sitting in a pod in position a at time t = 0 minutes, determine his position when he reaches b and e. o b: (1, 23) and e: (4, 38) o b: (4, 23) and e: (16, 38) o b: (1, 53) and e: (4, 68) o b: (4, 53) and e: (16, 68)

the graph shows a complete cycle of the sinusoidal function, representing the height of a ferris wheel with respect to time. a ferris wheel is 30 meters in diameter and is raised on a platform 8 feet from the ground so that the bottom of the wheel is in line with the top of the platform. a ride lasts 20 minutes and undergoes five revolutions in a clockwise direction during this time. if brad is sitting in a pod in position a at time t = 0 minutes, determine his position when he reaches b and e. o b: (1, 23) and e: (4, 38) o b: (4, 23) and e: (16, 38) o b: (1, 53) and e: (4, 68) o b: (4, 53) and e: (16, 68)

Answer

Answer:

A. B: (1, 23) and E: (4, 38)

Explanation:

Step1: Calculate period

The Ferris - wheel makes 5 revolutions in 20 minutes. So the period $T=\frac{20}{5}=4$ minutes.

Step2: Analyze position B

Position B is at $\frac{1}{4}$ of a revolution from A. Since the period is 4 minutes, the time to reach B is $t = \frac{1}{4}\times4 = 1$ minute. The height of the Ferris - wheel: The diameter is 30 meters and it is 8 meters above the ground. The center of the Ferris - wheel is at $h_0=8 + 15=23$ meters. At B, the height is the same as the center - height, so the height is 23 meters. So the position of B is (1, 23).

Step3: Analyze position E

Position E is at 1 full revolution from A. Since the period is 4 minutes, the time to reach E is $t = 4$ minutes. The maximum height of the Ferris - wheel is $h_{max}=8 + 30=38$ meters. So the position of E is (4, 38).