A Ferris wheel has a maximum height of 245 feet and a wheel diameter of 230 feet. Find an equation for the wheel if the center of the wheel is on the y-axis and y represents the height above the ground.
equation is ?
radius must be 115 ft
and its center must be 245-115 or 130 above the x-axis, (the ground)
equation:
x^2 + (y-130)^2 = 115^2 = 13225
see
http://www.wolframalpha.com/input/?i=x%5E2+%2B+%28y-130%29%5E2+%3D+13225
A Ferris wheel has a maximum height of 270 feet and a wheel diameter of 250 feet. Find an equation for the wheel if the center of the wheel is on the y-axis and y represents the height above the ground.
x^2 + (y-145)^2=15625
Well, if the center of the wheel is on the y-axis, we can say that the x-coordinate of any point on the Ferris wheel is always 0. Since y represents the height above the ground, we can say that the y-coordinate is the height of the Ferris wheel at any given point.
Now, since the maximum height of the Ferris wheel is 245 feet, we can set up the equation y = 245.
However, this equation only represents a single point on the Ferris wheel, which is when the wheel is at its highest point. To represent all the points, we need to consider the wheel's diameter.
The diameter of the wheel is 230 feet, which means the radius (half of the diameter) is 230/2 = 115 feet. Since the center of the wheel is on the y-axis, we can say that the distance from any point on the Ferris wheel to the center (y-coordinate) is the same as the radius.
Therefore, we can modify the equation to take into account the different heights as the wheel rotates:
y^2 + x^2 = r^2
Since the x-coordinate is always 0, the equation simplifies to:
y^2 = r^2
Substituting the value of the radius (115 feet), we have:
y^2 = 115^2
Simplifying further, we get:
y^2 = 13225
So, the equation for the Ferris wheel is y^2 = 13225.
To find the equation of the Ferris wheel, we can consider the center of the wheel as the origin, or the point (0, 0), since it is located on the y-axis. Let's assume that the wheel starts at its lowest point and rotates counterclockwise.
First, let's consider the diameter of the wheel, which is 230 feet. The diameter is the distance between two opposite points on the circumference of a circle. In this case, it represents the total vertical distance covered by the Ferris wheel from the lowest point to the highest point.
Since the center of the wheel is at the origin, the highest point will be at (0, h), where h represents the maximum height of the Ferris wheel, which is 245 feet. The lowest point will be at (0, -h).
Now, let's look at the relationship between the radius and the height. The radius of the wheel is half the diameter, so it is 230/2 = 115 feet.
As the wheel rotates counterclockwise, the height will vary based on the position of an individual point on the wheel's circumference. Let's call this position x, which represents the distance from the center of the wheel to a certain point on the circumference.
We can now see that as x varies from -115 to 115, the height y varies from -h to h. Therefore, we can express this relationship using an equation.
The equation for the Ferris wheel will be:
y = h * (x / 115)
In this equation, as x varies from -115 to 115, y will vary from -h to h, representing the height above the ground at different positions of the Ferris wheel.
Note: This equation assumes that the Ferris wheel does not experience any tilting or leaning effects while rotating.