# Thread: Ferris wheel problem calculus

1. ## Ferris wheel problem calculus

Hi, can someone help. A ferris wheel has a diameter of 40ft and its axle is 25 ft above the ground. Three seconds after it starts, your seat is at a high point. The wheel makes 3 rev/min. I know that the equation is 25 + 20cos(pi/10)(t-3). What is the fastest that the function changes? Where is the seat when the function changest the fastest? Please explain the last 2 questions.

2. Originally Posted by pantera
Hi, can someone help. A ferris wheel has a diameter of 40ft and its axle is 25 ft above the ground. Three seconds after it starts, your seat is at a high point. The wheel makes 3 rev/min. I know that the equation is 25 + 20cos(pi/10)(t-3). What is the fastest that the function changes? Where is the seat when the function changest the fastest? Please explain the last 2 questions.
You have:

$\displaystyle \theta(t)=\frac{\pi(t-3)}{10}$

$\displaystyle h(t)=25 + 20 \cos(\theta(t))$

The rate of change of height is $\displaystyle h'(t)$ and you need to find the maximum of this

$\displaystyle h'(t)=20 \sin(\theta(t))\ \frac{d\theta}{dt}=2 \pi \sin(\theta(t))$

and the maximum absolute value of this occurs when $\displaystyle \theta=\pi/2$ and $\displaystyle \theta=3\pi/2$

CB

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### ferris wheel precalc

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