# Ferris Wheel WS

• Jan 20th 2011, 10:59 AM
ASsdfghg
Ferris Wheel WS
Hi everyone, I have a WS due tomorrow, and would really appreciate some help.

You are taking a ride on a Ferris wheel that is 100 feet in diameter and has a bottom point that is 10 feet above the ground. Suppose that the wheel rotates four times every minute and from your friend's viewpoint on the ground, it is rotating in a clockwise direction.

1. Sketch your height y above the ground as it depends on the horizontal distance x from a vertical axis through center of the Ferris wheel.

2. Sketch your height y above the ground as a function of time t.

3. Find a formula for your height y as a function of t.

4. Sketch your horizontal distance x as a function of time t.

5. Find a formula for the horizontal distance x as a function of time t.

6. Find all intervals of time for which you are moving forward. Indicate these intervals on the graph in number 2.

7. Suppose your friends moves around the opposite side of the wheel so now it appears to him to be moving counter clockwise. From this new vantage point, how do your answers to number 6 change?

8. Find a formula relating your height y above the ground and horizontal distance x from the vertical axis through the center of the wheel.

I started by making a graph of the time (3.75, 7.5,11.25, and 15) for each rotation, the horiz distance from the y axis (don't know how to find) and the height (50,100,50,0). Any tips or solutions would be very much appreciated. Thanks!
• Jan 20th 2011, 12:11 PM
wonderboy1953
Quote:

Originally Posted by ASsdfghg
Hi everyone, I have a WS due tomorrow, and would really appreciate some help.

You are taking a ride on a Ferris wheel that is 100 feet in diameter and has a bottom point that is 10 feet above the ground. Suppose that the wheel rotates four times every minute and from your friend's viewpoint on the ground, it is rotating in a clockwise direction.

1. Sketch your height y above the ground as it depends on the horizontal distance x from a vertical axis through center of the Ferris wheel.

2. Sketch your height y above the ground as a function of time t.

3. Find a formula for your height y as a function of t.

4. Sketch your horizontal distance x as a function of time t.

5. Find a formula for the horizontal distance x as a function of time t.

6. Find all intervals of time for which you are moving forward. Indicate these intervals on the graph in number 2.

7. Suppose your friends moves around the opposite side of the wheel so now it appears to him to be moving counter clockwise. From this new vantage point, how do your answers to number 6 change?

8. Find a formula relating your height y above the ground and horizontal distance x from the vertical axis through the center of the wheel.

I started by making a graph of the time (3.75, 7.5,11.25, and 15) for each rotation, the horiz distance from the y axis (don't know how to find) and the height (50,100,50,0). Any tips or solutions would be very much appreciated. Thanks!

My comment is that a problem this complex should be broken down into parts (several threads) to be worked on in this website.
• Jan 20th 2011, 12:13 PM
Ackbeet
In addition, if this is a worksheet to be turned in for a grade, then you should know it is MHF policy not knowingly to help with such problems.
• Jan 20th 2011, 01:15 PM
emakarov
I agree with the previous posts. But I could not help myself:
Quote:

the wheel rotates four times every minute
This means that at the top one feels only about 2/3 of one's weight!
• Jan 20th 2011, 05:19 PM
homeylova223
I have a very similar problem in my text book I let me lend you a hand.
First we shall find the radius
A=1/2(100) which is 50 feet
Next we will find the period
2pi/k=4/1 since the wheel rotates 4 time is one minute
k=1/2pi
since it is ten feet of the ground your h will be 50+10=60 feet
You shall have no phase shift because equilibrium point is t=0
you will know have this function
y=50 sin (1/2pi)(T)+60
T will stand for your time
y shall give you the height
for example
100=50 sin(1/2pi)(T)+60
40=50 sin(1/2pi)(t)
arc sin(40/50)=(1/2pi)(t)
t=(1/2pi) arc-sin(40/50)
t= It will reach a height of 100 in 1 minute and 45 seconds
• Jan 20th 2011, 05:50 PM
skeeter
Quote:

Originally Posted by homeylova223
Next we will find the period
2pi/k=4/1 since the wheel rotates 4 time is one minute
k=1/2pi ... no

wheel rotates 4 times in one minute, period, T, is the time to complete one rotation ...
T = 15 seconds = 1/4 minute

$\displaystyle k = \frac{2\pi}{T}$

$\displaystyle k = \frac{2\pi}{15}$ if t is in seconds

$\displaystyle k = 8\pi$ if t is in minutes