What is 4/9 of 21???
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The 210 feet diameter of the ferris wheel rotated 45° gives;
The amount by which the height of the seat changes is the option;
- startfraction 210 startroot 2 endroot over 2 endfraction ft.
Given parameters;
Diameter of the wheel, <em>D </em>= 210 feet
Angle of rotation of the wheel = 45°
Required;
The measure by which the height changes.
Solution;
The equation of a Ferris wheel can be represented as follows;
y = A•sin(B•(x - c)) + D
Change in height, ∆y, is found as follows;
∆y = A•sin(t1) + D - A•sin(t2) + D
∆y = A•(sin(t1) - sin(t2))
Where;
t1 = 0
t2 = 45°
A = The radius = 210 feet
Therefore;
∆y = 210×2×(sin((45+0)/2)° × cos((45-0)/2)°)
∆y = 210×2×(sin(22.5)° × cos(22.5)°)
∆y = 210×sin(2×22.5)° = 210×sin(45)°
- ∆y = 210×(√2)/2
The amount by which the height of the seat changes is therefore;
The correct option is therefore;
startfraction 210 startroot 2 endroot over 2 endfraction ft.
Learn more about the equation of a Ferris wheel here:
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