Answer:
t = 2.9517 min
Step-by-step explanation:
Given
D = 40 m ⇒ R = D/2 = 40 m/2 = 20 m
ybottom = 2 m
ytop = ybottom + D = 40 m + 2 m = 42 m
yref = 34 m
t = 10 min
The height above the ground (y) is a sinusoidal function.
The minimum height is ybottom = 2 m
The maximum height is ytop = 42 m;
The midline is (ybottom + ytop)/2 = (2 m + 42 m)/2 = 22 m
If we model the wheel as follows
x² + y² = R²
where
y = yref - (R + ybottom) = 34 m - (20 m + 2 m) = 12 m
R = 20 m
we have
x² + (12 m)² = (20)²
⇒ x = 16 m
then
tan (θ/2) = x/y
⇒ tan (θ/2) = 16 m/12 m
⇒ θ = 106.26°
Knowing the angle of the circular sector, we apply the relation
t = (106.26°)*(10 min/360°)
⇒ t = 2.9517 min
Since the period of revolution is 10 minutes, the ride is above 34 meters for 2.9517 minutes each revolution.
