math real world by pearl

7/29/2019 Math Real World by Pearl

1/20

Pearl Sriorathaikul 10D

Real World

In this real world, it will investigate seeing how to use quadratics in real life. This

investigation will be on about basketball, bridge and drinking fountain. These main topics

will be discussed trying to find an answer to the questions and also explaining the accuracy

of it and how it can be applied in real life.

Watching Video 1

Some of the questions I could ask about the video before actually watching it are:

Will the positioning of the guy effect where the ball goes? How did he shoot the ball? What is the speed/force when the ball shoots? What is the weight of the ball? What is the angle of release? Was there spinning involved? What is the height of the basketball hoop? What are the different factors that determine whether the ball will get into the hoop

or not?

When I watched the video, there was an action shot of the guy jumping and the ball going

through mid-air, showing the path of where the ball takes off after the guy had shot the ball.

Below is the screenshot of the video and where it stopped. This video had made me think

about where the ball will land and if it will make it through the hoop or not.

After the video, I chose two questions that I found was interesting and important and

answered them:

What are the different factors that determine whether the ball will get into the hoopor not?


2/20


The height of which he throws the ball at, the amount of force he is using, the wind that is

affecting the ball, the velocity of the ball.

Will the positioning of the guy effect where the ball goes?The positioning of where the guy is of the utmost importance. A foot can mean thedifference in the effectiveness of where the ball goes. If the set is too low, you might find

your options limited.

Will the ball go into the hoop?I predict that the ball will go into the hoop since there is a lot of indication from the

different balls that there is a chance of it going into the hoop. From the balls in the picture

that show a pathway helps into seeing that there is a high possible chance for the ball to go

into the hoop. The pathway of the basketballs is also making a curve which is possible since

the curve goes straight through the hoop.

I experimented with the website http://www.geogebratube.org/student/m3660 and I

moved the points of each of the sliders, adjusting it so that there is a curve going through

the balls and into the basketball hoop. The sliders in the GeoGebra control the steepness of

the line. The h controls the positioning of the vertex on the x axis and the k controls the

vertex on the y axis. At first when I tried it I got a completely different rule but I later

realized what each of the sliders (a, h, k) meant and after that I tried adjusting the slider

points to make the curve to go through the ball which can affect the outcome of the rule. So

then the rule was found as seen from the screenshot below.

Rule : Y= -0.08(x-19.1)2

+ 14.25


3/20


The basketball hoop (seeing if it works or not).

I am going to write down the equation and plot it down as a graph to prove whether or not

the ball will land into the basket.

Y= -0.08 (x-10.10)

2

+ 14.25

Y= -0.08 (x2-20.2x+ 102.01) + 14.25

Y= -0.08x2+ 1.616x-8.1608 + 14.25

Y= -0.08x2+1.616x+6.0892

It is proven again that the ball will go into the basket from the formula given and there is a

100% chance of the ball shooting right into it and not missing the hoop.


4/20


Do your answers make sense? How do you know?

The answer makes sense and the ball went into the hoop. I chose this question since I

thought was the most important question to find out and most relatable to the real world in

finding if the ball will go into the hoop or not. I know that the answers make sense since the

GeoGebra was tested out showing the curve of the ball going into the basketball and it

makes sense for the ball to go into the basket as well as the equation works in general, and

it is reasonable.

How accurate are your answers? How do you know?

The more basketballs shown on the picture, the more accurate the direction will be. Since

one ball will be harder to predict because we dont know where the ball will go (either going

higher in a loop or curve). As shown, there is more balls added in the picture and the

direction gets clearer and that the direction is more specific which can be easier to identify

whether the ball goes in or not and that has a good effect on the accuracy as well of gettinga good view of the directions. The answer was accurate since a graph was checked upon

with using the same rule and there was also a curve indicating the ball going into the basket.

When GeoGebra was being used, it showed a path of the curve going through the ball and

into the basket whether than adjusting the sliders and the line not going through all of the

balls would also make it less accurate. But the answer is quite accurate but it isnt

guaranteed since the numbers for GeoGebra is only rounded up to two decimal places.

Could you have found more accurate answers? How?

Yes, finding accurate answers all depend on the values presented and what information the

task has provided. Simply, the values in the GeoGebra are rounded up to only two decimal

points which do not guarantee that the data is accurate. Rounding off numbers only give an

approximate value. Therefore, assuming that the values in the GeoGebra are accurate

cannot become a valid argument. Rather than using GeoGebra, using other forms and

methods of calculation can also check if the formula that is found for the parabola is correct

and accurate.


5/20


I watched Video 3 and my answer turned out to be right! The ball shot right into the hoop

and what I did on GeoGebra earlier turned out to be exact. Below is the photo of the video

of the ball going into the hoop.

3. Finding the track of the ball Where it Lands

I went to the Geo Gebra site http://www.geogebratube.org/student/m10515. I followed the

instructions given below the page. The data was entered into the table on the right hand

corner. I used the points in GeoGebra to gather data on the flight of the ball and find a

function to fit. The data that was entered is shown below:


6/20


Dropping into the bin? Using the

point to calculate

I will be focusing on whether the ball will land into the bin or not and by finding that, I will

have to find out the points of the bin using the red point and keying it into the graph.

After entering the data in the table, and then using the two value regression tool to fit to a

quadratic, the equation can be seen. I later found whether the ball was going to land into

the bin or not. This was found by getting the red point and moving it over to the bin and it

formulates the answer and proves that the ball will land in the bin seen in the graph below.


7/20


Even though I thought my answers were correct and that the ball was going to land I tried

plugging in the equations from the graph into the Input box I later found that the ball goes

into the bin but isnt accurate and all the data wasnt keyed in at first. I thought that the ball

would land in the bin but later on realized that the points werent all recorded for the value

of each of the balls which gives an un-accurate answer. From this, I tried again and tried to

be more accurate so that I get a better result. Below is a screenshot of what turned out to

be an incorrect answer.

I tried it AGAIN using the red point and counting all the balls of the pathways shown now:

Above is the screenshot which can be seen on the right of the picture is the graph of which

are the numbers of each of the points of the ball all calculated and written into the data Aand B.


8/20


After all the information was entered into the table, the two value regression tool was used

to fit to a quadratic and the screenshot above from the Regression Analysis Graph show

gives an equation showing it is a quadratic. From this, using the equation to write into the

Input Box to figure out whether or not the ball will land into the bin.


9/20


So this is a more accurate data and shows the curve of where the ball will land, which from

this data shows that the ball will obviously not land into the bin as predicted.

Answer: The ball will not land into the bin

This answer makes sense. This is because there is a curve onto the ball which shows thatthe ball doesnt go into the bin as show in the screenshots above. This answer can be seen

from the equation from the graph which clearly shows a curve of where the ball will

eventually end up going to (direction).

The answers werent very accurate since there werent that many points shown in the

picture to have calculated a better view of where the ball might land to. By that, it decreases

the chance of the accuracy but also some accuracy like getting the points onto the white

dots on the picture and giving out the number, writing the data shows accuracy since there

is no need to count it reading the x and y axis and instead it gives out the exact data for the

points (red point). But other than that there should be a clearer pathway to the bin and the

dots werent as clear.Even though most of it isnt as clear, there were some things that canstill prove that there was some accuracy which was the dots as mentioned earlier which

helped out in trying to find the most accurate rule.

I could have found more accurate answers by trying to find new ways of getting the points

to all be more accurate and trying to get the points all in a line and adding them into the

picture to maybe give guidance in which the ball will be landing or not. But another way of

being more accurate is there should be the GeoGebra site with this picture where there are

sliders and curves to help indicate whether the ball will go into the bin or not which might

be very helpful at this stage.


10/20


Part 2-

1. Bridge

Questions I could have asked for the bridge:

What is the highest point of the bridge? How long is the whole bridge? How much weight can the bridge hold? How much weight can it hold at a specific location vs. the whole bridge? What is the distance along the point of the bridge in the middle? How long is the bridge from the stand to the other? How high is the bridge?

Answering the question:

I chose an important/ interesting question I found and I thought I wanted to find out for

myself and see whether I would be able to answer it or not. My question is:

What is the highest point of the bridge?In the bridge folder, the document labeled Bridge Dimensions is a guide to answering the

question. Below is the picture from the document which was given.


11/20


From that picture, it is later saved onto the desktop as a picture file and then later following

the instructions from the PDF how to insert pictures using GeoGebra to find the answer.

From this data I am able to plot my answers into the computer from each of the points in

order to find a curve.

Calculator:

I used the calculator to find the rule for the equation of the curve. I keyed in the data for all

the points, and from that I got the results for a, b and c which is a co-efficient for y=ax2+bx+c.

In order to find the highest point, I must key in the equation into GeoGebra from the

information from the calculator which is:

Y= .0690592306x2+-.4203513244x+.7436940437

From keying that equation into GeoGebra, a curve is shown as shown below in the

screenshot from GeoGebra.


12/20


From that, I will find the highest point of the bridge of the actual measurements:

Horizontal Distance (Point)/Horizontal Distance (Real) = 6.1-0.08/1280 = 6.02/1280

Vertical Distance (Point)/Vertical Distance (Real) = 0.7-0/x = 0.7/x

6.02/1280 = 0.7/x

6.02 x = 0.7 * 1280

x = 0.7x1280/6.02

x = 148.84 m

From my calculations, it is proven that the highest point of the bridge for the actual

measurements would have to be 148.84 meters.

Do your answers make sense? How do you know?

My answers do make sense and I know this because I have used the ratio theorem to prove

that the height is 148.84 m which is reasonable height. Also the equation was clearly shown

from the calculator and graph as well which proves that it does make sense.

How accurate are your answers? How do you know?

My answers arent that accurate since the point isnt very clear and it might have not been

as accurate since the points might have not been on the exact line as moved. But from that,

the calculator indicates some accuracy from typing in the results and getting a good

equation to find the curve of the line. The tool that was used to help me calculate the data

for this particular scenario was only an assumed value which makes it difficult to find theactual precise numeral value for the position of the points.


13/20


How accurate do you need to be? Why?

You need to be accurate when pointing the dots since it will affect the outcome of the

answers which will not get the results to be right.

Could you have found more accurate answers? Why?

I could have found accurate answers, yes. This can be more accurate by trying to get the

dots onto the point and trying it many times to see the results since my photo when I

zoomed in the points werent exactly on the dot which might affect.

2. Drinking Fountains

I used the website http://academic.sun.ac.za/mathed/Shoma/Fountain.htm, and I followed

the instructions in order to find an equation for this photo:

The photograph shows the water that is squirting from a drinking fountain. And the task is

using the knowledge of graphs in finding a function y= f(x) that models the curve formed by

the squirting water. The coordinates of the points are show at the bottom, helping to find

the equation. In order to gather data from the picture, then use this data in order to find an

algebraic formula modeling (Entering in the Domain minimum and Domain maximum).

After the numbers have been keyed in, I clicked on the Excel squirt button in order to

further find an equation for the water. There is a graph being imported to excel during this

process and from the graph of the website that was given, it gave exact equations andnumbers to prove and help find the equation.


14/20


Below is the graph:

With this information, I have used it to create an equation. From this answer, the equation

is:

-0.0045x2+2.319x+-92.85

After that I entered in the Domain minimum, domain maximum and the function (equation

that I got) and from that I found out that the formula is correct.


15/20


Checking my model:

From that it can be shown that:

The equation is accurate and the graph shown is possible since the data is clearly labeled on

the sides of which the blue and red line is and also it is the best fit. This site was pretty

accurate since there were good instructions and everything was clear and numbers

appeared when moving the lines in the water fountain picture around. There was also an

Input Box which helped to check out the equation and see if the red curve will be straight

through the water fountain.

What are the important mathematical ideas that you have used?

Being able to apply some of the mathematical concepts to this investigation is crucial. The

most important concept is applying quadratic equations and formulas to be able to

determine the curve (parabola) of a certain object.

3. Moving Pictures- BMX Bike (Challenge Question)

BMX biking is the sport of racing bicycles in motocross style on tracks which use an inline

start and have obstacles. It is designed for dirt and motocross cycling.

To be a successful BMX biker, you must have the ability to control the direction of the bike

and you need to be able to have muscular power, muscular endurance, and muscular

strength and speed as well. You also need to be able to handle the bike on the dirt terrain.

You can find alternative sports to be able to improve speed in cycling and muscles like

cycling normally on a concrete terrain or weight lifting can also help with the lower muscles

of the body. People choose to run or swim in order to improve their muscle endurance,

strength and power. Since BMX Races are often on the dirt terrain, this means that the biker

should be able to train on the course around once a week in order in getting used to it and

building the correct muscles. Having recovery periods will help as well because training

everyday can be very tiring and can often reduce the performance rate of the biker.


16/20


If you were a BMX rider what information about the dirt jumps and riders flight path would help

you in your training?

Being able to know the gradient of the jumps and the distance between the two can help

the rider prepare and calculate how fast they have to accelerate before the jump and how

they have to position their bike before facing each obstacles.

What information do you need?

In order to actually find which one the better biker is, you will need to know the height that

you go up the highest and whether or not the biker as successfully being able to balance

their control.

Before I start comparing these two jumps and plotting the graph, I am going to predict who

the better biker is from watching the video.

From looking closely at the video, the better biker would be Ben Dirt Jump 22. This would

have to be because he is able to move up higher than the second biker and is able to do

tricks that will help him land properly and easily.

I followed the instructions Logo Pro Video Analysis in order to find the points for the graph

and able to get a curve that will determine for both videos of Ben Dirt Jump 22 and Ahmed

Dirt Jump 25, which is the better biker.

Ben Dirt Jump 22 (1)-

I followed the instructions of the video by adding in the video from the Insert Movie and

later plotted the points of the video and once the graph is shown, I clicked on the Curve Fit

button in order to get a Quadratic and click try fit. The screenshot below indicates once I

have clicked on the button At^2+Bt+C equation and clicked on try fit. The coefficients

besides are the values for A, B and C.


17/20


From that, below is the graph which shows where the curve is and tells the co-efficient.

-

Ahmed Dirt Jump 25 (2)-

I did the same thing as the video Ben Dirt Jump 22 in order to find the curve fit for the

jump. Below is an example of what I did for the video in order to find the curve and get a

graph that will help to determine the coefficient for the equations.


18/20


As seen below is after clicking the Curve Fit button and showing what I did in order to get a

graph with the curve and the coefficients:

This is what the graph looks like for Ahmed Dirt Jump 25:

Comparing


19/20


Ben Dirt Jump 21 (1) Ahmed Dirt Jump 25 (2)

Above is the comparison graph of Ben Dirt Jump 21 and Ahmed Dirt Jump 25. Ben Dirt Jump.

The graph one indicates the curve of the highest point at 380 m and Graph two indicates the

curve of the highest point at 300 m. Ahmed Dirt Jump 25s Graph compared to Ben Dirt

Jump 21s graph seems like the jumping highest distance isnt that different but when

reading the y axis, it indicates that Ben Dirt Jump 21s graph goes up to 400 m while Ahmed

Dirt Jump 25s graph only goes up to around about 310 m.

This then proves that Ben is the better biker.

How accurate are your answers?

My answers arent that accurate. One of the factors that affect the accuracy would have to

be the quality of the video. Since both of these videos are blurry and pixelated, this would

make it harder to watch and find the points in which the biker travels from one point to

another when pointing the values. Since the points arent as accurate, the curve would

change and this will affect the equation of the parabola as well. So the video really makes a

difference to the accuracy.

What other methods could you have used to find an answer?Other methods that could be used to find an answer would be to use the calculator in which

can help find out the parabola of the curve which can give an accurate answer of the

equation and make the accuracy of the whole question greater.

If you found equations for the two jumps, what other information could you obtain from

the equations?

If we have the equation of the parabola of the two bicycle riders, we are then able to find

the horizontal distance of the two bikers. I am able to then compare who is able to drive the

bicycle further as well.


20/20


How would this type of information be useful for the bike riders?

The information that was applied in this section of the investigation makes bmx cycling a lot

more fun and safe. People are now able to calculate the distances they have to travel as well

as the pathway that they should take in order to land safely on the other side of the course.

Without having prior knowledge on calculating the pathways and distances, bmx cycling can

reduce the number of fatalities and injuries amongst those who are participating in the

games.

Conclusion

The graph of a parabola defines various kinds of curves related to every day events and real-

world objects. Even when you throw a ball or an object, the path of the objects flight

through the air is shown as a parabola. All objects that take flight usually have its climax

point as the highest point of their curves, as seen in the different scenarios. Real life

parabolas include mirror found in a cars headlight and the flight of a certain object. The

rules and answers in the investigation made sense,and accuracy was not a major issue withthe task. The methods for some of the main ideas arent the most efficient, as finding the

rule might have been quicker but wouldnt have allowed me to understand where the rule

came from. By being able to self-discover and investigate the core roots of the formulas and

concepts, I am able to enhance my understanding in this area of algebra. If you have

different curves, you are able to find parabola equations and you can find out the highest

and lowest points that can help in construction, velocity of the airplane and sports like

biking in real life. In conclusive, every mathematic concept, from addition to quadratic

equations can be applied in real life anywhere and anytime.

math real world by pearl

Documents