Step-by-step explanation:
General form of a sine or cosine wave is:
y = ±A sin((2π/T) t) + B
y = ±A cos((2π/T) t) + B
where A is the amplitude, T is the period, and B is the vertical offset or midline.
The Ferris wheel is 80 meters in diameter or 40 meters in radius.
A = 40
The Ferris wheel turns once every 8 minutes.
T = 8
The lowest point is 5 meters above the ground, so the center of the Ferris wheel is 45 meters above the ground.
B = 45
At t=0, you're at the lowest point, so use -cos.
Therefore, the equation is:
y = -40 cos(2π/8 t) + 45
y = -40 cos(π/4 t) + 45
When t = 5:
y = -40 cos(5π/4) + 45
y = 20√2 + 45
y ≈ 73.3 meters
When y = 35:
35 = -40 cos(π/4 t) + 45
-10 = -40 cos(π/4 t)
1/4 = cos(π/4 t)
π/4 t ≈ 1.318
t ≈ 1.68 minutes
