Question

The distance from the ground of a person riding on a Ferris wheel can be modeled by the equation d equals 30 times the sine of the quantity pi over 20 times t end quantity plus 15 comma where d represents the distance, in feet, of the person above the ground after t seconds. How long will it take for the Ferris wheel to make one revolution?

Answer 1

40 seconds

Explanation:

You have a Ferris wheel such that the height of a rider is modeled by d=30sin(πt/20)+15, and you want to know the time it takes for one revolution.

Periodicity

The sine function has a period of 2π. The value of the function when the argument is 2π is the same as when it is zero. The period is the time difference between those argument values. Since the argument is 0 when t=0, we only need to find the value of t that makes the argument 2π:

2π = πt/20

40 = t . . . . . . . multiply by 20/π

The Ferris wheel makes one revolution in 40 seconds.