A Ferris wheel is 36 meters in diameter and boarded from a platform that is 1 meter above the ground. The six o’clock position of the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 9 minutes. What is the height of the rider after 2 minutes into the ride?
36 meters in diameter ... A=18
y = 18sin(x)
board on a platform that is 1 meter above the ground.
y = 19 - 18cos(x)
1 full revolution in 9 minutes
y = 19 - 18cos(2π/9 x)
now you know all about the function.
To find the height of the rider after 2 minutes into the ride, we first need to determine the position of the Ferris wheel after 2 minutes.
Since the Ferris wheel completes 1 full revolution in 9 minutes, we can calculate the number of revolutions it makes in 2 minutes by dividing 2 by 9:
2 minutes / 9 minutes/revolution = 2/9 of a revolution
Next, we need to calculate the angle corresponding to 2/9 of a revolution. Since a full revolution is 360 degrees, we can multiply 360 degrees by 2/9:
360 degrees * 2/9 = 80 degrees
So, after 2 minutes, the Ferris wheel is at an angle of 80 degrees.
Now, let's use the given information about the Ferris wheel to find the height of the rider at this angle.
The diameter of the Ferris wheel is 36 meters, which means the radius is half of the diameter, or 36/2 = 18 meters. Since the rider boards the Ferris wheel from a platform that is 1 meter above the ground, the initial height is 1 meter.
To find the height of the rider after 2 minutes, we can use basic trigonometry. The height can be determined by calculating the sine of the angle and multiplying it by the radius:
Height = sin(angle) * radius
Height = sin(80 degrees) * 18 meters
Using a calculator or mathematical software, we find that sin(80 degrees) ≈ 0.9848.
Height = 0.9848 * 18 meters
Height ≈ 17.728 meters
Therefore, the height of the rider after 2 minutes into the ride is approximately 17.728 meters.