A Ferris Wheel is....

Question

A Ferris wheel is 35 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 6 minutes. How many minutes of the ride are spent higher than 38 meters above the ground?

--- minutes 

Answer 1

This is not hard to solve but writing out the solution may be tricky.

You need to draw a figure.

When the riders are 16.5 m above the center of the Ferris wheel, they will be 34 m above the ride entrance and therefore 38 m above the ground.

 

On your figure draw the diameter from the entrance point (the line between 12 and 6 on a clock).

The point where the riders are 16.5 m above the ground is about 11 o'clock.

Draw the radius to that point and then the line parallel to the diameter between 12 and 6; the length of this line must be 16.5 m in order for the riders to be high enough.

In the small triangle call θ the angle at the apex of the triangle; θ = arc cos (16.5/17.5) = 19.46°.

Therefore during an angle of 38.92° (from approximately 11 o'clock to 1 o'clock) the riders are above 38 m.

Thus for 38.92/360 of every 6 minutes the riders are above 38 meters; this amounts to above .64 minutes of each cycle.

Answer 2

Solution withdrawn. Mistake made on circumference. Look at Paul's solution. That's the correct solution.