A Ferris wheel is 50 meters in diameter and boarded from a platform that is 4 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 52 meters above the ground?

To determine how many minutes of the ride are spent higher than 52 meters above the ground, we need to calculate the time it takes for the Ferris wheel to reach that height during one revolution.

First, let's find the radius of the Ferris wheel. The diameter is given as 50 meters, so the radius would be half of that, which is 25 meters.

To find the time it takes for the Ferris wheel to reach a height of 52 meters, we need to calculate the angle at which the Ferris wheel is at that height. At the six o'clock position, the Ferris wheel is level with the loading platform, which is 4 meters above the ground. So, the height difference from the six o'clock position to 52 meters above the ground is 52 - 4 = 48 meters.

To calculate the angle, we can use the formula:

angle = arc length / radius

Since the arc length is equal to the height difference of 48 meters, we can substitute this value in:

angle = 48 meters / 25 meters

angle ≈ 1.92 radians

Now, we know the angle at which the Ferris wheel reaches a height of 52 meters. The Ferris wheel completes one full revolution in 8 minutes, which is equivalent to 2π radians.

To find the time it takes for the Ferris wheel to reach this angle, we can set up a proportion:

time / 2π = angle / (2π)

Simplifying the proportion:

time = (angle * 2π) / (2π)

time = angle

time ≈ 1.92 radians

Therefore, it takes approximately 1.92 minutes for the Ferris wheel to reach a height higher than 52 meters above the ground during one complete revolution.

Please note that this calculation assumes a constant speed for the Ferris wheel and neglects any acceleration or deceleration effects.

the center of the wheel is 29 m above the ground ... 50/2 + 4

using the center of the wheel as the origin, higher than 52 m means y > 23

y/r is the sine of the central angle for h > 52

the wheel rotates at ... 360º per (8*60) sec

find the time it takes to pass through the angle for h>52