Pre Calc Question

Question

Assume the 3 o'clock position on a ferris wheel is level with the loading platform and that the ferris wheel travels in the counter-clockwise direction. The wheel rotates 27π/4 radians and then stops for 2 hours for repair work. At what time would the ferris wheel be stopped for two hours for repair work?

Answer 1

2π radians is equal to 360 degrees (a full rotation).

27π/4 radians = (27/4)π radians = (6 3/4)π radians = 3(2π radians) + (3/8)(2π radians)

Six and 3/4 radians is 3 full rotations and 3/8 more of a rotation.

So,3 full rotations, then (3/8)*360 = 135° degrees more.

135º = 90º + 45º [That is, move from 3 o'clock to 12 o'clock, then to 10:30 o'clock.

That puts the spot on the ferris wheel at 10:30 o'clock for maintenance.