A Ferris wheel's boarding platform is 1 meters above the ground, has a diameter of 46 meters, and rotates once every 6 minutes.
How many minutes of the ride are spent higher than 26 meters above the ground?
radius = 23, period = 6, so k = π/3, so the height of the seat at time t is
h(t) = 24 - 23cos(π/3 t)
How long does it take to get up to 26m?
24 - 23cos(π/3 t) = 26
t = 1.58
so the time spent above 26m is 6 - 2*1.58 = 2.83 minutes
To answer this question, we need to determine how long the riders on the Ferris wheel spend at heights higher than 26 meters above the ground.
First, let's find the distance between the lowest point of the Ferris wheel and the ground. The boarding platform is located 1 meter above the ground, so the lowest point of the Ferris wheel is 1 meter above the ground level.
Next, we find the highest point of the Ferris wheel. The Ferris wheel has a diameter of 46 meters, so the radius is half of the diameter, which is 23 meters. The highest point of the Ferris wheel is therefore 23 meters higher than the lowest point. Adding the 1 meter from the ground, the highest point is 24 meters above the ground.
Now, we can calculate the time spent above 26 meters. We subtract the height of the lowest point (1 meter) from the height of the cutoff point (26 meters) to get 25 meters. This means we need to find how long it takes for the Ferris wheel to cover 25 meters in its rotation.
The Ferris wheel completes one full rotation in 6 minutes. To calculate the time spent above 26 meters, we need to figure out what fraction of the total distance is covered by 25 meters. The circumference of a circle (which represents the path of the Ferris wheel) is given by the formula C = 2πr, where r is the radius. In this case, r = 23 meters. Therefore, the circumference is equal to 2 * π * 23 meters.
To find the fraction of the circumference covered by 25 meters, we divide 25 meters by the circumference of the circle and multiply by the time for one complete rotation, which is 6 minutes:
(Time spent above 26 meters) = (25 meters / (2 * π * 23 meters)) * 6 minutes
Calculating this equation will give us the number of minutes riders spend above 26 meters on the Ferris wheel.