Farris wheel modeling question

Question

A farris wheel is 30 meters in diameter and sits on a 2 meter high platform. 6 o'clock position is is level with the platform. After 10 minutes it makes 1 complete rotation. How many minutes of the ride are spent higher than 24 meters above ground?

Answer 1

Steven G's explanation is great for figuring out the problem algebraically/mathematically. I hope this offers an explanation of how it might look visually...

You might start by graphing the circle represented by the ferris wheel on a cartesian plane. Consider the x-axis to be the ground. The center of your circle should be (0,17), with a radius of 15. Then draw a horizontal line across your graph at y=24 and the mark its points of intersection with your circle as A & B. Now, consider that the ferris wheel is a clock whose hands rotate every 10 min instead of 60 min. How many minutes are there between A & B, above the line y=24?

I hope this helps. Please let us know if you need further assistance.

Answer 2

Assume that the center, C, of wheel is on the ground and the problem ask for how many minutes are you 7 m above the ground.

The equation of the wheel is x^2+y^2 = 15^2 = 225

Find where this wheel (circle) intersects the line y=7. This will give you two points, say A and B. Now draw lines AC and BC. Find the measure of the angle ACB, call this value t radians

Then the answer will be 10*( t/(2pi))