Question

Alf a passenger rides counter-clockwise from point m to point j, approximately how many feet has the passenger traveled?

Answer 1

We have to calculate how many feet the passenger traveled from M to J.

This distance is the arc length between M to J.

To calculate the arc length between two points on the circle, we need the central angle measure of the arc and the radius length.

As each seat is equidistant, we assme that each pair of seat has a constant central angle.

There are 18 sectors, so each sector will represent an angle of 360° / 18 = 20° per sector.

Now, we count how many sectors have between M to J, following the trajectory of the seat (counterclockwise):

We have 14 sectors that will represent a central angle of 14*20° = 280°.

Then, we can calculate the arc length as:

`\begin{gathered} L=f\cdot C \\ L=(280)/(360)\cdot2\pi r \\ L=(14)/(18)\cdot2\pi\cdot200 \\ L\approx977.38 \end{gathered}`

To calculate it we use the fraction of the arc measure relative to the full circle measure.

We then multiply this fraction by the circumference of the wheel and obtain the arc length.

Answer: 977.38 feet.