The Singapore Flyer, currently the world's largest Ferris wheel, completes one rotation every 37 minutes. Measuring 150m 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 9.25 minutes.
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To determine the o'clock position on the Singapore Flyer and the height above the ground of a person who has ridden the wheel for 9.25 minutes, we need to calculate the fraction of a complete rotation that has occurred in that time.
The Singapore Flyer takes 37 minutes to complete one full rotation. Therefore, in 9.25 minutes, it would have completed:
9.25 minutes / 37 minutes = 0.25 rotations
Since the wheel turns in the clockwise direction when viewed from Marina Centre, we can determine the o'clock position by multiplying the fraction of a rotation by 12 (since a clock has 12 hours).
0.25 rotations * 12 hours = 3 hours
Thus, the o'clock position on the wheel would be at approximately 3 o'clock.
Moving on to determine the height above the ground, we need to calculate the distance covered based on the time traveled. Since each rotation of the Flyer covers the circumference of the wheel, which has a diameter of 150m, the distance covered in each rotation is:
Circumference = π * diameter
Circumference = 3.14 * 150m
Circumference = 471m (approximately)
To find the distance covered in 9.25 minutes, we can calculate the fraction of a rotation and multiply it by the circumference:
Distance covered = Fraction of rotation * Circumference
Distance covered = 0.25 rotations * 471m
Distance covered = 117.75m (approximately)
Therefore, a person who has ridden the wheel for 9.25 minutes would be located approximately at a height of 117.75m above the ground.