ferris wheel totaldoc

8/14/2019 Ferris Wheel Totaldoc

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Sydney SunKappa3/19/08

High Dive Unit

Problem:

Can we Save

Andre?


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Sydney Sun

Kappa

3/14/08

Problem Statement

On the day of the CAT-nival, Andre Howard plans to jump off of the Farrell

Ferris Wheel. At the same time there is a cart of water that is traveling from the

left of the wheel to right. And, Andres objective is to jump off of the FF Wheel

and land in to the cart of water. My job, is to figure out how long Andre should be

on the FF wheel before be dives so that hell land exactly into the pool. Also, my

calculations need to be as correct as possible so that I can both assure Andre

that my calculations are correct and that Andre will be alive after the jump is done

and over with.

I know and found out that the Farrell Ferris Wheel has a 50foot radius,

which means that the wheel also has a 100-feet diameter (but we won t be using

that bit of information in this problem). The FF Wheel is on a 15 feet stand, which

makes the distance from the center of the wheel to the ground 65 feet. I also

know that the FF wheel isnt sporadic and that it turns at a constant speed,

which, makes one complete turn in 40 seconds. The wheel also completes this

turn counter clockwise. The cart of water that Andre is jumping into is 240 feet to

the left of the FF wheel. The cart moves 15feet per second and has a water level

of 8 feet off of the ground. I also know that Andre is standing at the 3o clock

position on the FF wheel.


3/9

I will need the final equation that we had already figured out which iscos

(9w)50=-240+15(w+57+15(9w)/16. There are 2 ways that I can solve this

problem. I can either use Guess and Check, or I can try to figure out another

way.

Sydney Sun


4/9

Kappa

3/16/08

Work Section

In solving the unit problem, there were a lot of equations that were

involved in the process. But, the thing is the main equation that we used was

our final equation which is cos(9w)50=-240+15(w+57+15(9w)/16. This equation

is a culmination of other equations. In that equation, 50 is the radius, W is wheel

time, the 9 is degrees per second, the 15 is the rate of the pool, and the -240 is

the starting point of the pool. The final equation is made up of the equation for

height, falling time, and cosine.

The first equation that I had figured out/used is the equation for falling

time. I had gotten this equation from our very first class work. The equation is

t=h/16. In this equation t stands for time, which is the thing that I was looking

for. The h stands for height, which the distance that the object is from the

ground. The 16 is half of the rate that and object falls at32 everything falls at

the same rate against gravity, and that rate is 16. The process that I took find

this equation was:

Steps

1) h-16t^2=0 2) 16t^2/16=-h/16 3) t^2=-h/16 4)t^2=-h/16 5) t=h/16

The second equation that I had found was the equation for height, which,

is h(t)=65+50sin(9t). Once again h is height, t is time, and 9 is the degrees

per second. The 65 represents 65ft, which is the center of the Ferris wheel to the


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ground, and the 50 represents the radius of the Ferris Wheel. Those 2 numbers

were given to us. Also, in the unit problem, we used sine and cosine because

they are 2 trigonometry functions that would help us find the triangle that will be

created between the ground, the height and where Andre will be. Also, Cosine

gives me the X position(horizontal) and Sine will gives me the Y position

(vertical).

Also, Trigonometry is the study of how the sides and angles of a triangle are

related to each other. So, one would assume that Trig only has to do with

triangles, but trig also has to do with circles because, If the length of the

hypotenuse(longest side of a triangle) is exactly one unit, we call the circle that

the end of the hypotenuse draws, a unit circle.

Cosine

Sin

e

50 Ft

65 ft

cart


6/9

Unlike my original plan, I had to reconstruct the final equation. I tried to

enter it into the calculator as it was, but it didnt work. Later on I figured out that I

had to change the equation according to PEMDAS because that is how the

calculator will read it. That was a step that I had to my original plan, or I wouldnt

have been able to solve the Unit Problem. So, I had to figure out where each

parenthesis will be and everything. I went from this equation cos(9w)50=-240+15

(w+57+15(9w)/16 to (( sin(9w)50+57)/16+x), I entered the new equation as Y1

in the graphing calculator and I entered cos(15+-240) as my second line. After I

just graphed it and the calculator found the point of intersection, which was

12.282855 for X and -17.54771 for Y.

Sydney Sun

Kappa


7/9

3/16/08

Answer Section

After doing extensive math computation. I had found the answer:

X= 12.282855

Y= -17.54771

I know my answer is right because I had correctly altered the Final Equation

according to PEMDAS, which was (( sin(9w)50+57)/16+x), And since I know

that the graphing calculators follow PEMDAS, I know that I got the answer

correct. Before that I also know that I got the answer right because all of the

equations that I used were also correct the falling time equation and height

equation were both correct and I also used Sine and Cosine correctly. So, I did

not make a mathematical mistake on my path to solving the Unit problem and

saving Andres life.

Sydney Sun

Kappa


8/9

3/18/08

Reflection

When I had first gotten the problem I thought it was going to be the

hardest problem that I would ever solve in my life. I was never really comfortable

with Trig. I didnt understand Sine and Cosine I couldnt really even differentiate

between the different sides of the triangle. So, I was really nervous embarking

on the unit problem. But after I had finished the first class work and the first

home work and the 2nd and the 3rd I realized that I was doing pretty well and I

actually understood what I was doing as long as I concentrated and didnt over

think and over complicate things. Then, when we all as a class went over

everything that we had done and how they all connect with one another I

understood what I had to do. Then after we had done all of the work that we did,

and we started the Unit Circle I knew that I didnt want to do guess and check.

Mostly because I knew that I didnt have the patience for it and I thought that

there had to be another way because the entire time we were figuring out the

class work you (Ms. Farrell) always told us not to over complicate things. Also, at

the bottom of the page PEMDAS was written there and I thought that there had

to be a reason why that was there and there had to be a connection and after

thinking a while I got it.

I learned that one of the initial inaccuracies that I had in my original plan

was that I didnt take into account how the Calculator computates. It actually

took me a while before I figured out that that was the problem I was having. I

kept on entering the equation into the calculator. Then I realized the issue and


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the thing with PEMDAS, and I made the alterations and I got the right answer. I

feel like part of the reason why I did waste so much time, was because I didnt

think my plan through as well as I could have. I should have thought about every

variable that would affect my plan before I started, but I didnt, so I had to find the

solution on the spot.

A situation that would change my answer is if the speed of the Ferris

wheel changes. It would change my final answer because the Ferris wheel

would either be faster or slower and that would change the degrees per second.

So, anywhere in the equation that has a 9, it would change, and that would effect

the time at which Andre would be dropped, and the relationship between the

Ferris wheel and the cart will also change.

2 real world situations that I could apply this math to are, 1) in the future if

I decide to open my open cookie company and get and work a cookie conveyer

belt I have to figure out how fast I need to collect cookies keeping the cookie

stamp and the belt in mind so that I dont back up the cookies. The other real

world example if I go to a BBQ and we all decide to play a game where people

form 2 lines face one another and throw footballs toward the center where 1

person would have to run through. I could use this math to figure out the speed

that the 2 rows would throw the ball at and when it will hit me so that I can avoid

the balls so I dont get hurt.

ferris wheel totaldoc

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