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SEL17 · May 23, 2010, 03:13 PM

have been staring a my notes and this question for a while now, and I CAN'T get I. Please help me!

Jack decides to ride the Ferris wheel. He boards the ride at 1m and is the last person on the ride. The diameter of the wheel is 16m and it takes 8 sec for one complete revolution. Find the equation that represents Jack's height in relation to time. Then use the equation to determine Jack's height after 35sec.

I think I will be bale to answer the second part of the question on my own. But I honestly can't get the equation. I have no idea what I am doing wrong.

ArcSine · May 23, 2010, 03:57 PM

Couple o' hints: First, picture the wheel (as viewed from the side) as a unit circle centered at the origin. In such a construct, Jack's height could be given as sin(x), and his height would thus vary from -1 to +1.

Thus, this basic sine function needs to be 'expanded' (using the factor A) and vertically shifted up (via some constant B) so that Jack's height will peak at 17 and bottom out at +1...

Height = Asin(argument) + B

Next, you'll need to find an argument for that sine function--with t as the variable, representing time in seconds--so that as t runs from 0 to 8, the entire 'inside' argument runs from -pi/2 to 2pi - pi/2. In other words, getting Jack from the bottom of the circle at t=0 all the way back around to the bottom again at t=8.

Unknown008 · May 24, 2010, 07:26 AM

In fact, it is in the form of:

$Height = A sin(t+B) + C$

where the constants are A, B and C. A sine curve starts at y = 0, but here, knowing that the range of a sine curve varies between -1 and 1, 0 represents the halfway up height of Jack.

If you prefer using another trigonometric ratio for that, you can use the negative cosine ratio, and then, you will not need the 'B' constant within the ratio here.

$Height = -Acos(t) + C$

In this case, A and C in either formula has the same value.

galactus · May 24, 2010, 10:08 AM

Here is a very nice site explaining it with nice Applets. You can easily find the function that represents your wheel by looking here:

Teaching Math: Grades 9-12: Representation

Click on 'See Example' to whatch the graph of the wheels motion being drawn.

It even has a double ferris wheel, which is more complicated.