A Ferris wheel is 25 meters in diameter and boarded from a platform that is 2 meters above the ground. The six o'clock position on the Ferris wheel is level with the loading platform. The wheel completes 1 full revolution in 8 minutes. How many minutes of the ride are spent higher than 26 meters above the ground?
y = 14.5 - 12.5cos(π/4 x)
so, you want to solve
14.5 - 12.5cos(π/4 x) = 26
cos(π/4 x) = -23/25
π/4 x = π ± 0.407
...
You want the interval between those two solutions
How did you get the ending side
To solve this problem, let's break it down step by step:
Step 1: Calculate the height of the Ferris wheel from the ground.
Since the platform is located 2 meters above the ground, we need to add this height to the radius of the Ferris wheel. The radius is half of the diameter, so in this case, it would be 25/2 = 12.5 meters.
Adding the platform height, the total height of the Ferris wheel from the ground is 12.5 + 2 = 14.5 meters.
Step 2: Calculate the highest point of the Ferris wheel.
The highest point of the Ferris wheel occurs when it is at the 12 o'clock position. At this point, the radius of the Ferris wheel is equal to the height from the ground.
So, the highest point of the Ferris wheel is 14.5 meters above the ground.
Step 3: Calculate the lowest point of the Ferris wheel.
The lowest point of the Ferris wheel occurs when it is at the 6 o'clock position. At this point, the radius of the Ferris wheel is equal to the height from the ground.
So, the lowest point of the Ferris wheel is 14.5 meters above the ground.
Step 4: Calculate the range of the ride above 26 meters.
In this case, we want to know the duration when the ride is higher than 26 meters above the ground. To find this, we need to determine the number of revolutions the Ferris wheel makes.
Since the Ferris wheel completes 1 full revolution in 8 minutes, we can calculate the number of revolutions during the ride. Let's assume the ride lasts for t minutes.
The number of revolutions can be found by dividing the total time by the time for each revolution:
Number of revolutions = t / 8.
Step 5: Calculate the time spent higher than 26 meters.
To find the time spent higher than 26 meters, we need to calculate the fraction of the ride that is spent between 26 meters and the highest point of the Ferris wheel.
The range above 26 meters can be calculated by finding the difference between the highest point of the Ferris wheel and 26 meters:
Range above 26 meters = 14.5 - 26 = -11.5 meters.
However, since the range should be positive, we take the absolute value of the negative value:
Range above 26 meters = 11.5 meters.
Now, we can calculate the time spent higher than 26 meters by multiplying the range by the number of revolutions:
Time spent higher than 26 meters = Range above 26 meters * Number of revolutions.
Finally, substitute the values into the formula and calculate the result based on the given information.