A Ferris wheel has a diameter of 30 m, with the center 18 m above the ground. It

Question

A Ferris wheel has a diameter of 30 m, with the center 18 m above the ground. It makes one complete rotation every 60 s. Draw the graph of one complete cycle, assuming the rider starts at the lowest point. Find the cosine equation of the graph. What is the height of the rider at 52 seconds? At what time (s) is the rider at 20 m? A Ferris wheel has a radius of 35 m and starts 2 m above the ground. It rotates once every 53 seconds. Sketch 2 complete cycles of the graph. Determine the cosine equation of the graph. What is the height of the rider at 81 seconds? At what time does the rider reach a height of 51 m?

Explanation / Answer

1) b)   h = 15*cos((pi/30)*t) + 18

c) At t = 52 s =====> h = 15*cos(pi*52/30) + 18 = 28 m

d) 20 = 15*cos((pi/30)*t) + 18

       0.133 = cos((pi/30)*t) =========> t = 13.7 s and 46.3 s

2) since cos(x) starts at a maximum, you must have -cos(x)
The radius is 35, so   y = -35cos(x)
It starts at y=2, so the axle is at y=37:
y = 37-35cos(x)
The period is 53, so
y = 37-35cos(2pi/53 x)

c) At x = 81 s ====> y = 71.45 m

d) 51 =  37-35cos(2pi/53 x) ======> x = 16.72 s

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