a. One rotation of the wheel starting at the lowest point would look like a sinusoidal curve that starts at the bottom (lowest point), goes up to the highest point, comes back down to the lowest point, and completes one full cycle.
b. The equation of the function that represents the height of a seat on the Ferris wheel can be represented as:
Height = 9sin(π𝑡/30) + 10.4
c. To calculate the height of a seat after 50 seconds, we substitute 𝑡 = 50 into the equation:
Height = 9sin(π(50)/30) + 10.4
Height = 9sin(5π/3) + 10.4
Height = 9sin(300°) + 10.4
Height = 9sin(60°) + 10.4
Height = 9(√3/2) + 10.4
Height = 4.5√3 + 10.4
Height ≈ 17.17 meters
Therefore, the height of a seat after 50 seconds would be approximately 17.17 meters.
Answer a series of questions about each of the following four scenarios.
1. The height of a seat on a Ferris wheel varies sinusoidally with time (𝑡) in seconds. The wheel has a radius of 9 𝑚𝑚, and it rotates once every 60 seconds. Passengers get on at the boarding platform, which is 1.4 𝑚 above the ground.
a. show one rotation of the wheel starting at the lowest point.
b. Write the equation of the function that represents the graph.
c. Calculate the height of a seat after 50 seconds.
1 answer