Welcome to our page: Maths in Sports!
What do we want to achieve?
We are Jikke, Nina, Marit, Lex and Job and we want to know what the perfect throw in a basketball game is. Therefore we need to do a bit of research and apply some things we learned in Mathematics. We are going to lead you trough our journey of finding the perfect throw!
Get to know us
JikkeHi! I am Jikke and really enjoy doing this. In this project I am the group leader and I will help my friends out!
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JobHello, I am Job and I actually play football, I think you will question yourself why I actually chose this sport? Well, that is pretty simple, I like everything that has to do with sports! In this project I will gather information about basketball.
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NinaHello! I am Nina and I like this for real. it is different than the normal math lessons. Together with Job and Marit I will gather information.
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MaritMy name is Marit. I totally agree with Jikke, and my task is to gather some information with Nina and Job.
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LexHello! My name is Lex and I play basketball myself! My task is to edit this webpage and to give this project a nice look.
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"Weeblee sounds stupid, can't they think of another name?" ~ Jikke
Oops, bloopers!
"Nooo Lex.... Why did you make this video :)" ~ Marit
Our Formula
In this formula we are going to calculate the perfect free throw when standing on the free throw line.
We first made some measurements:
- The basket is 3.05 meters high
- Our shooter has the ball at a hight of 1.50 meters
- He stood away 4.6 meters from the basket (on the free throw line)
- The turning point of the ball was at 1.5 meters on the x-axis and at a height of 3.6 meters on the y-axis
To really calculate this, we thought of a picture.
We first made some measurements:
- The basket is 3.05 meters high
- Our shooter has the ball at a hight of 1.50 meters
- He stood away 4.6 meters from the basket (on the free throw line)
- The turning point of the ball was at 1.5 meters on the x-axis and at a height of 3.6 meters on the y-axis
To really calculate this, we thought of a picture.
"B-B-B-Basketball...." ~ Lex
In this sketch we visualized the information given.
In the sketch you can see that we used the Y-axis as the wall that interferes with the basket. This means that the interception with the Y-axis is equal to 3.05 meters. We used the ground as our X-axis.
our formula is as followed:
f(x) = a(x-p)^2 + q
In here we will substitute our information. To fill in the numbers; a , p and q we need to know some of the coordinates of the parabola.
These are as followed:
- (1.5 , 3.6) The turning point of the ball
- (0 , 3.05) The height of the basket
- (4.6 , 1.5) This is the distance from the basket and the height where the start position of the ball will be.
With these coordinates we can calculate the formula. The coordinates of the turning point are p and q, so then we can change the formula as followed: f(x) = a(x - 1.5)^2 + 3.6
The formula isn't completed yet because we don't have point a.
We can generate point a by substituting the other coordinates into the formula.
The formula now looks like this:
3.05 = a(0 - 1.5)^2 + 3.6
3.05 = 2.25a + 3.6
-2.25a = 0.55
a = -0.244
Finally we can complete our formula.
Now it looks as followed:
f(x) = -0.244(x - 1.5)^ + 3.6
In the sketch you can see that we used the Y-axis as the wall that interferes with the basket. This means that the interception with the Y-axis is equal to 3.05 meters. We used the ground as our X-axis.
our formula is as followed:
f(x) = a(x-p)^2 + q
In here we will substitute our information. To fill in the numbers; a , p and q we need to know some of the coordinates of the parabola.
These are as followed:
- (1.5 , 3.6) The turning point of the ball
- (0 , 3.05) The height of the basket
- (4.6 , 1.5) This is the distance from the basket and the height where the start position of the ball will be.
With these coordinates we can calculate the formula. The coordinates of the turning point are p and q, so then we can change the formula as followed: f(x) = a(x - 1.5)^2 + 3.6
The formula isn't completed yet because we don't have point a.
We can generate point a by substituting the other coordinates into the formula.
The formula now looks like this:
3.05 = a(0 - 1.5)^2 + 3.6
3.05 = 2.25a + 3.6
-2.25a = 0.55
a = -0.244
Finally we can complete our formula.
Now it looks as followed:
f(x) = -0.244(x - 1.5)^ + 3.6
"Why are basketballs orange?" ~ Job
Conclusion
Does a "golden throw" exist? We don't think so. There are a lot of different options and methods to throw the basketball into the basket, so there isn't a "special" way where you will allways throw the ball into the basket. We think it just needs a lot of practice and effort!
Comparison
The other groups put great effort into their projects as well! It looks absolutely fantastic and comprehensive, because of a nice mixture between layout, personalization and information.
Similarities:
- All the projects show a lot of good information
- The projects are made really well. Everybody had good arguments and showed a lot of additional information
Differences:
- One group had a lot of variation, they didn't choose one sport, but chose a big amount of them!
All in all, everybody did a great job!
Similarities:
- All the projects show a lot of good information
- The projects are made really well. Everybody had good arguments and showed a lot of additional information
Differences:
- One group had a lot of variation, they didn't choose one sport, but chose a big amount of them!
All in all, everybody did a great job!
Reflection
How our group worked out? Our group worked out absolutely fantastic! Everybody did their task and nobody wasn't doing nothing. In the first lesson we divided our tasks. Nina and Marit would create a formula and they did this perfectly. Jikke, Lex and Job went to the gym to gather information and make a short movie. We really enjoyed it and it was a nice way to be busy with two different subjects, physical education and mathematics! We had a lot of fun in doing this and we hope it can be repeated more often.
The end
This was our maths project! We hope you enjoyed it. We did for sure!
Made with a little bit of love by: Jikke, Nina, Marit, Job and Lex from 3TT2