A ferris wheel is 35 meters in diameter and boarded at ground level. The wheel makes one full rotation every 8 minutes, and at time t = 0 you are at the 9 o'clock position and descending. Let f (t) denote your height (in meters) above ground at t minutes. Find a formula for f (t).

Question

Mathematics

Anna Jacobson

20 November, 23:26

A ferris wheel is 35 meters in diameter and boarded at ground level. The wheel makes one full rotation every 8 minutes, and at time t = 0 you are at the 9 o'clock position and descending. Let f (t) denote your height (in meters) above ground at t minutes. Find a formula for f (t).

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Answers (2)

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Darwin · Answer 1

F (t) = - 17.5sin ((t/4) * pi) + 17.5

Because the ferris wheel is a circle you can use sine and cosine. As we are descending and in the middle of the descent the use of negative sine makes the most sense.

Period = 2pi.

Our period is 8 minutes.

8 minutes*w = 2pi

w = (t/4) * pi.

The 17.5 at the end is to take into account that we are 17.5 meteres up in the air at the start.

Audrina · Answer 2

I personally think it is f (t) = 17.5 sin (π/4) (-t+6) + 17.5