The Singapore Flyer, currently the world's largest Ferris wheel, completes one rotation every 37 minutes.1 Measuring 150 m in diameter, the Flyer is set atop a terminal building, with a total height of 165 m from the ground to the top of the wheel. When viewed from Marina Centre, it turns in the clockwise direction. State the o'clock position on the wheel and height above the ground of a person who has ridden the wheel for 27.75 minutes.
What position is the person in? (choose one)
a)the person is in the 9 o'clock position
b)the person is in the 12 o'clock position
c)the person is in the 3 o'clock position
d)the person is in the 6 o'clock position
How to calculate the height
Height = ______ m
To determine the position of a person who has ridden the Singapore Flyer for 27.75 minutes, we can use proportions based on the time it takes to complete one full rotation.
Given that the Singapore Flyer completes one rotation in 37 minutes, we can set up the proportion:
37 minutes = 360 degrees
27.75 minutes = ? degrees
To solve for the angle the person has traveled, we can cross-multiply and divide:
27.75 minutes * 360 degrees = 37 minutes * ?
This simplifies to:
9,990 degrees = 37 minutes * ?
Next, we divide both sides of the equation by 37 minutes:
9,990 degrees / 37 minutes = ?
This gives us the angle in degrees that the person has traveled on the Singapore Flyer in 27.75 minutes. To find the corresponding position on the wheel, we need to determine how many degrees correspond to each position on the clock face.
Since there are 12 positions on a clock face (12 o'clock, 1 o'clock, 2 o'clock, and so on), the degrees per position can be calculated:
360 degrees / 12 positions = 30 degrees per position
Therefore, each position on the wheel corresponds to 30 degrees.
Now, we can divide the angle traveled by 30 degrees to find the position on the wheel (clock face):
(9,990 degrees / 30 degrees per position) = ?
This calculation yields:
333 positions = ?
Since we want to determine the specific o'clock position, we need to divide the number of positions by 30:
333 positions / 30 positions per hour (o'clock) = ?
This gives us:
11.1 hours = ?
Since the calculated value is in decimal form, we can convert it to time format:
0.1 * 60 minutes = 6 minutes
Therefore, the person who has ridden the Singapore Flyer for 27.75 minutes is in the 11 o'clock position.
To calculate the height above the ground of the person, we need to determine the fraction of the total time it takes to complete one rotation and multiply it by the total height of the wheel.
Fraction of time traveled = 27.75 minutes / 37 minutes
Height above the ground = Fraction of time traveled * Total height of the wheel
Height above the ground = (27.75 minutes / 37 minutes) * 165 m
Height above the ground = (0.75) * 165 m
Height above the ground = 123.75 m
Therefore, the person who has ridden the Singapore Flyer for 27.75 minutes is in the 11 o'clock position and approximately 123.75 meters above the ground.