the ferris wheel first appeared at the 1893 chicago exposition. its axle was 45 feet long. spokes radiated…

the ferris wheel first appeared at the 1893 chicago exposition. its axle was 45 feet long. spokes radiated from it that supported 36 wooden cars, which could hold 60 people each. the diameter of the wheel itself was 250 feet. suppose the axle was located at the origin. given that the starting point is at the loading platform, find the location of the car at the 270° counterclockwise rotation position.

the ferris wheel first appeared at the 1893 chicago exposition. its axle was 45 feet long. spokes radiated from it that supported 36 wooden cars, which could hold 60 people each. the diameter of the wheel itself was 250 feet. suppose the axle was located at the origin. given that the starting point is at the loading platform, find the location of the car at the 270° counterclockwise rotation position.

Answer

Explanation:

Step 1: Determine the radius of the Ferris wheel

The diameter is 250 feet, so the radius ( r = \frac{250}{2} = 125 ) feet.

Step 2: Convert rotation angle to standard position coordinates

A 270° counterclockwise rotation from the starting point (loading platform, typically at 0° on the positive x-axis) places the car at an angle of 270°. Using polar coordinates ((r\cos\theta, r\sin\theta)):

  • ( \cos(270^\circ) = 0 )
  • ( \sin(270^\circ) = -1 )

Step 3: Calculate x and y coordinates

[ x = r\cos\theta = 125 \times 0 = 0 ] [ y = r\sin\theta = 125 \times (-1) = -125 ]

Answer:

(0, -125)