Precalculus Trigonometry

Question

A Ferris wheel is 12 meters in diameter and makes one counterclockwise revolution every 6 minutes. Given that riders board the Ferris wheel at ground level, how long does it take for a rider to go from ground level to a height of 9 meters?

It takes____Minutes

Answer 1

You can model the Ferris wheel with a sine function. The rate of the wheel is 2π/6 = π/3. Let t = time in minutes. At t=0, the Ferris wheel car will be at the bottom of the circle, or at -π/2. This would be the phase shift of the sine function. So the model would be

y(t) = 6sin(πt/3 - π/2) + 6.

y(0) = -6 +6 = 0.

y(3) = 6sin(π-π/2) + 6 = 6+6 = 12 --> top of Ferris wheel

For y = 10:

-6sin(πt/3 - π/2) + 6 = 10 --> sin(πt/3 -π/2) = -4/6 = -2/3

arcsin(-2/3) = -0.7297 = -0.23π = πt/3 - π/2 ---> t = .73π(3/π) = 2.19 minutes

It takes 2.19 Minutes

Answer 2

Let's say you wanted to go 3/4 of the way around. That would be 3/4 times the circumference.

The circumference is 12π. The portion of that circumference is 9/(12π).

6[9/(12π)] = 1.43 mins

0.43(60) = 26 seconds

1 minute and 26 seconds