Re: Amusement park problem.

What have you tried?

Where are you stuck?

Re: Amusement park problem.

I'm stuck at relating the rate of degrees per second with the rate of change in height per second.

Re: Amusement park problem.

For a circle with center at (0, 17) and diameter 34, we can write parametric equations

$\displaystyle x= 17 cos(\theta)$

$\displaystyle y= 17 sin(\theta)+ 17$

where $\displaystyle \theta$ is the angle a radius makes with the horizontal.

Re: Amusement park problem.

I'm still confused. How do I calculate the height?

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Re: Amusement park problem.

draw a sketch for the height of the seat as a function of time ...

you know the period and can calculate the amplitude of vertical motion.

'

Re: Amusement park problem.

The amplitude would be 19 feet, right? And the period would be 360degrees?

Re: Amusement park problem.

Quote:

Originally Posted by

**explodingtoenails** The amplitude would be 19 feet, right? And the period would be 360degrees?

amplitude is correct ... the period is how long it takes (time) to complete one revolution.

Re: Amusement park problem.

So the period is 1 minute?

Re: Amusement park problem.

Quote:

Originally Posted by

**explodingtoenails** So the period is 1 minute?

quoted from your problem statement ...

Quote:

A particular wheel has a diameter of 38 feet and **travels at a rate of 4 revolutions per minute**.

try again. how long does it take to complete one revolution?

Re: Amusement park problem.

So the period is 15 seconds?

Re: Amusement park problem.

Correct, for the function $\displaystyle \cos nx $ the period is given as $\displaystyle p= \frac{2\pi}{n}$

You know p=15, solve for n.

Re: Amusement park problem.

Re: Amusement park problem.

Quote:

Originally Posted by

**explodingtoenails** n = 2pi/15 ?

why are you unsure?

are you familiar with the general form of y = Acos[B(t+C)] + D and what each of A,B,C, and D represent?

Re: Amusement park problem.

Mhm, I know that equation.

If the y-axis is h and the x-axis is t, would the equation be:

h(t) = 19cos24t - 19

I did the - 19 because the graph starts in the negatives.