Jamie rides a Ferris wheel for five minutes. The diameter of the wheel is 10 meters,and its center is 6 meters above the ground. Each revolution of the wheel takes 30 seconds. Being more than 9 meters above the ground causes Jamie to suffer an anxiety attack. For
how many seconds does Jamie feel uncomfortable?
draw a triangle from the diameter horizontal, up from the horizontal 3m to intersect the circle, then the hyp is the radius back to the center.
h=3m so 3/5 = sinTheta theta= 36.8deg
So the person is below nine meters then the bottom 180deg, and the top each side 36.8 deg, or a total of 253.7 deg, or
253.7/360 percent of the time.
time above= 5min*253.7/360
To determine the time Jamie feels uncomfortable, we need to find out how many revolutions of the Ferris wheel cause them to be more than 9 meters above the ground.
First, let's calculate the circumference of the Ferris wheel. The circumference is equal to the diameter multiplied by π (approximately 3.14):
Circumference = 10 meters * π ≈ 31.4 meters
Next, we divide the circumference by the distance covered per revolution:
Revolutions = Circumference / Distance per revolution
Since each revolution takes 30 seconds, the distance covered per revolution can be calculated as follows:
Distance per revolution = Diameter * π ≈ 10 meters * π ≈ 31.4 meters
Revolutions = 31.4 meters / 31.4 meters = 1 revolution
This means that Jamie is more than 9 meters above the ground for one revolution of the Ferris wheel.
Since each revolution takes 30 seconds and Jamie rides the Ferris wheel for 5 minutes (or 300 seconds), the number of revolutions during this time period can be found by dividing the total time by the time per revolution:
Number of revolutions = 300 seconds / 30 seconds = 10 revolutions
However, we are only interested in the number of revolutions that cause Jamie to be more than 9 meters above the ground. Since this only occurs for one revolution, the number of seconds Jamie feels uncomfortable is:
Seconds feeling uncomfortable = Number of revolutions * Time per revolution
= 1 revolution * 30 seconds
= 30 seconds
Therefore, Jamie feels uncomfortable for 30 seconds.
To find out how many seconds Jamie feels uncomfortable, we need to determine how long he is at a height greater than 9 meters above the ground while riding the Ferris wheel.
First, let's find the circumference of the Ferris wheel. The circumference is the distance traveled in one revolution and can be calculated using the formula:
Circumference = π * Diameter
Given that the diameter of the wheel is 10 meters, we can calculate the circumference:
Circumference = π * 10 = 31.42 meters (approximately)
Since each revolution of the wheel takes 30 seconds, Jamie spends 30 seconds for one complete round trip on the Ferris wheel.
Now, let's determine at what heights Jamie experiences discomfort. The center of the wheel is 6 meters above the ground, so the wheel's highest point is at 6 + (10/2) = 11 meters above the ground.
Therefore, Jamie will feel anxious during the time he spends at a height above 9 meters but below 11 meters.
To determine the time spent in this uncomfortable height range, we can calculate the arc length based on the angle covered by Jamie's uncomfortable height range.
The angle of the uncomfortable height range can be calculated using the formula:
Angle = (Uncomfortable Height Range) / Diameter * 360
Angle = (11 - 9) / 10 * 360 = 72 degrees
The arc length covered by Jamie's uncomfortable height range can be calculated using the formula:
Arc Length = (Angle / 360) * Circumference
Arc Length = (72 / 360) * 31.42 ≈ 6.28 meters
As Jamie spends 30 seconds for one complete revolution, the time spent in the uncomfortable height range can be calculated using the ratio of the arc length of the uncomfortable height range to the circumference:
Time spent in uncomfortable height range = (Arc Length / Circumference) * 30
Time spent in uncomfortable height range = (6.28 / 31.42) * 30 ≈ 6 seconds
Therefore, Jamie feels uncomfortable for approximately 6 seconds while riding the Ferris wheel.