A Ferris wheel is 35 meters in diameter and boarded from a platform that is 3 meters above the ground.

Question

A Ferris wheel is 35 meters in diameter and boarded from a platform that is 3 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 4 minutes. How many minutes of the ride are spent higher than 37 meters above the ground?

Answer 1

The is easier to visualize with a diagram, which I can't draw here. Let's start with the fact that the Ferris wheel spends the top half of the time half the time above 38 meters (3 meters for the platform, and 35 more to the centerline). So, we need to figure out how much time is spent one meter below the 9 oclock to 3 oclock period.

. So, now is time for the sketch. Draw a radius to a point a little below the 9 o'clock point on the circle Call that point A. I'll also call the point 8:58 to remind us that it is ALMOST at 9 oclock Draw a second radius directly to the 9 oclock point.. From the 9 oclock point drop a line perpendicular to the radius O-A. Define that perpendicular line as 1 meter. Then Point A defines the portion of the circle where the wheel is below the 9-3 diameter by one meter.

Noe we have an acute triangle with the following dimensions: Hypotenuse is O-A Radius(35 m), and the opposite side is 1 meter. Taking the Arcsin of 1/35 yields an angle of 1.64 degrees. So the wheel is below 37 meters for 1.64 degrees + 180 degrees (from 9 to 3) + another 1.64 degrees on the 3:02 side.

That's 183.28 degrees above 37 meters.

Finally 183.24/ 360 x 4 minutes yields 2.04 minutes.