# Pre-Calc

posted by John

A ferris wheel is 63 feet tall when it reaches its highest point at 8 seconds. At the bottom of the ride, you are 3 feet off the ground. So how high off the ground will you be 5 seconds after the ride starts?
Write a function f so that f(t) will equal how high in feet you will be off the ground t seconds later.

So I think the diameter is 60 feet meaning my radius is 30.And at the highest point, it takes me 8 seconds, so a full revolution must be 16 seconds. How do i make a equation to find how high I'll be 5 seconds later when I start from the bottom?

amplitude=30
Period=2π/16
Is this right?

1. Steve

since cos(kt) has its max at t=0, and you want your max at t=8, then using your correct amplitude and period, we have

y = 33 + 30cos((pi/8)(t-8))

So, now just plug in t=5 to answer the question.

You can see the graph at

http://www.wolframalpha.com/input/?i=33%2B30cos%28%28pi%2F8%29%28x-8%29%29

2. John

when i plug in t=5, I get 62.99 feet, but isn't that the height when t=8 seconds?

3. Steve

well, geez. when t=8, y=33+30cos(0) = 63

Isn't that what you wanted, the max height at t=8?

4. John

Sorry, I'll be more clear. The question already stated how high the ferris wheel is at t=8 seconds. The highest point the ferris wheel reaches is 63 feet and the time for that is 8 seconds. What I'm trying to find out is how high the ferris wheel is when t=5 seconds using an equation I can plug in.

5. Reiny

John, I don't know how you got 63 when t=5
I got 44.48 when t = 5

We could have used a sine curve

height = 30sin ((πt/8)(t-4) ) +33

check:
when t = 0 , height = 3 , ok
when t = 8 , height = 63, ok
when t = 4, height = 4.48 , the same result we get when we use Steve's cosine function.

6. John

Yeah sorry, my bad. I must have plugged in the numbers wrong, since I just got 44.5 for my answer. You guys are right, Thanks so much Steve and Reiny for your help!

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