The rim of the London Eye (a 135m diameter ferris wheel) moves 26 cm/sec, slow enough for passengers to safely get on the wheel from the platform (2 meters above ground level) without stopping the wheel at the bottom of its rotation.
What's the height at the bottom of the wheel? The top? How high above the ground is the center of the wheel?
How far does a passenger travel as the wheel makes one complete revolution? How much times does that take?
The height at the bottom of the wheel is 2 m; The height at the top is 2 + diameter = 137; The height at the center of the wheel is 2 + radius = 2 + 135/2
The circumference of the London Eye is 2*PI*r = PI*diameter = 135*PI. This is how far a passenger travels as the wheel makes one complete revolution. This takes (135*PI m)/(0.26 m/s)
To find the height at the bottom of the wheel, we need to consider the diameter of the ferris wheel. The diameter is the double the radius, so the radius of the wheel is 135m/2 = 67.5m.
At the bottom of the wheel:
Height = Ground level + Radius of the wheel
Height = 2m + 67.5m
Height = 69.5m
So, the height at the bottom of the wheel is 69.5 meters.
To find the height at the top of the wheel, we can use the same logic as above.
At the top of the wheel:
Height = Ground level + Diameter of the wheel
Height = 2m + 135m
Height = 137m
So, the height at the top of the wheel is 137 meters.
To find the height above the ground of the center of the wheel, we can simply use the radius of the wheel.
Height of center = Ground level + Radius of the wheel
Height of center = 2m + 67.5m
Height of center = 69.5m
So, the center of the wheel is 69.5 meters above the ground.
To find how far a passenger travels as the wheel makes one complete revolution, we need to find the circumference of the wheel. The circumference is given by the formula C = 2πr, where r is the radius of the wheel.
C = 2π * 67.5m
C ≈ 425.54m
Therefore, a passenger travels approximately 425.54 meters as the wheel makes one complete revolution.
To find how much time it takes for the wheel to make one complete revolution, we can divide the circumference by the speed at which the rim moves.
Time = Circumference / Speed
Time = 425.54m / 26cm/sec
To perform the calculation, we need to convert the speed to meters per second. Since 1 meter is equal to 100 centimeters, the speed in meters per second is 26cm/sec * (1m/100cm) = 0.26m/sec.
Time = 425.54m / 0.26m/sec
Time ≈ 1636.38 seconds
Therefore, it takes approximately 1636.38 seconds for the wheel to make one complete revolution.