Basketball Court Dimensions and Hoop Height: A Quick Guide
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How Big is a Basketball Court?
An NBA basketball court is 94 feet long and 50 feet wide. In meters, it’s 28.65 m long and 15.24 m wide. The WNBA and NCAA use an identical court size—94 feet long by 50 feet wide.
High school courts are a bit shorter, measuring 84 feet long by 50 feet wide. Junior high courts are even smaller, typically measuring 74 feet long and 42 feet wide. A FIBA court (used during international play such as the Olympics) is 91.86 feet long and 49.21 feet wide.
How Tall is a Basketball Hoop?
For junior high, high school, NCAA, WNBA, NBA and FIBA, the rim is exactly 10 feet off the ground. Rims at every level of play are 18 inches in diameter. Backboards are also the same size at each of these levels. A regulation backboard measures 6 feet wide and 42 inches (3.5 feet) tall.
What is the Distance of the 3-Point Line?
The 3-point line distance varies among different levels of play. The NBA 3-point line is 23.75 feet from the hoop, 22 feet in the corners. The FIBA 3-point line is 22.15 feet from the hoop, 21.65 feet in the corners. The WNBA uses the same 3-point line as FIBA.
At the NCAA level, the 3-point line distance is 20.75 feet, for both men and women. At the high school level, the 3-point line distance is 19.75 feet, for both boys and girls. Junior high uses the same 3-point line distance as high school.
What is Distance of the Free-Throw Line?
The distance of the free-throw line is measured from a point on the floor directly below the backboard. At the junior high, high school, NCAA, WNBA and NBA levels, the free-throw line is 15 feet away from this point. At the FIBA level, the free-throw line is actually a bit further—15.09 feet from the point.
How Big is The Key?
The size of the key, also commonly referred to as “the paint,” varies among levels of play. In the NBA, it’s 16 feet wide. Same goes for the WNBA. In FIBA, it’s 16.08 feet wide. At the NCAA level, the key is 12 feet wide. High school and junior high school use the same size key as the NCAA.
READ MORE:
Basketball Sizes: A Quick Guide for All Levels of Play
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How Big is a Basketball Court?
An NBA basketball court is 94 feet long and 50 feet wide. In meters, it’s 28.65 m long and 15.24 m wide. The WNBA and NCAA use an identical court size—94 feet long by 50 feet wide.
High school courts are a bit shorter, measuring 84 feet long by 50 feet wide. Junior high courts are even smaller, typically measuring 74 feet long and 42 feet wide. A FIBA court (used during international play such as the Olympics) is 91.86 feet long and 49. 21 feet wide.
How Tall is a Basketball Hoop?
For junior high, high school, NCAA, WNBA, NBA and FIBA, the rim is exactly 10 feet off the ground. Rims at every level of play are 18 inches in diameter. Backboards are also the same size at each of these levels. A regulation backboard measures 6 feet wide and 42 inches (3.5 feet) tall.
What is the Distance of the 3-Point Line?
The 3-point line distance varies among different levels of play. The NBA 3-point line is 23.75 feet from the hoop, 22 feet in the corners. The FIBA 3-point line is 22.15 feet from the hoop, 21.65 feet in the corners. The WNBA uses the same 3-point line as FIBA.
At the NCAA level, the 3-point line distance is 20.75 feet, for both men and women. At the high school level, the 3-point line distance is 19.75 feet, for both boys and girls. Junior high uses the same 3-point line distance as high school.
What is Distance of the Free-Throw Line?
The distance of the free-throw line is measured from a point on the floor directly below the backboard. At the junior high, high school, NCAA, WNBA and NBA levels, the free-throw line is 15 feet away from this point. At the FIBA level, the free-throw line is actually a bit further—15.09 feet from the point.
How Big is The Key?
The size of the key, also commonly referred to as “the paint,” varies among levels of play. In the NBA, it’s 16 feet wide. Same goes for the WNBA. In FIBA, it’s 16.08 feet wide. At the NCAA level, the key is 12 feet wide. High school and junior high school use the same size key as the NCAA.
READ MORE:
Basketball Sizes: A Quick Guide for All Levels of Play
What is AAU Basketball?
4 Youth Basketball Drills that Teach the Fundamentals
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Everything You Need to Know About Basketball Court Dimensions
Of the two major American-invented sports — baseball and basketball — only one has gained worldwide popularity. We play baseball across parts of the globe, but we play basketball worldwide. You can play with as few as two people and as many as ten. Shoot hoops indoors and outdoors and on any surface hard or flat enough to bounce a ball.
Indoor courts are usually made from hardwood, though other, more easily-maintained surfaces are gaining in popularity. Outdoor courts can be either asphalt or concrete. You can put a permanent basketball court just about anywhere you would like. Don’t have the room for a full-length court? Fitting just a half court into your driveway, backyard, or commercial gym would be just as useful.
So, have a space in mind and wondering “What are the dimensions of a basketball court?” Let’s take a look at the standard sizes for every level of basketball, from high school all the way up through international competition.
NBA Basketball Court Dimensions
The National Basketball Association, better known as the NBA, boasts the largest court dimensions of any level of basketball — domestic or international. The outer dimensions are 94 feet long by 50 feet wide. The half court line is, as the name would suggest, halfway between each end line. In the middle of the half court line is a tip-off circle with a six-foot radius, which often sports the home team’s logo.
The key is 16 feet wide and 19 feet from the baseline to the foul line. A semicircle with a six-foot radius extends from the foul line. Some courts have the other side of the half-circle drawn in a dotted line inside the key to complete the circle and create a clear boundary for any jump balls.
The backboard protrudes four feet out from the baseline, and the rim of the basket hangs 10 feet off the ground. Subtracting the four feet overhang from the 19-foot length of the key, we get the familiar 15-foot distance from the foul line to the front of the backboard. It’s a misconception that the foul line is 15 feet from the center of the basket. The backboard itself measures six feet wide and 42 inches high.
Inside the key, a four-foot arc is aligned with the center of the basket to designate the restricted arc. If a defender is inside this semicircle, he cannot draw a charging foul. Along both sides of the key, lines are drawn three feet apart to create the standing positions for other players during a free throw attempt, starting with a box that is seven feet from the baseline and one foot wide.
Outside the key, the three-point line forms an imperfect arc stretching one side of the baseline to the other. The arc isn’t a perfect circle because it would run out of bounds on the sides of the court.
Instead, the three-point line runs in a straight line from the baseline out 16 feet, nine inches, at which point the line begins to curve. The straight lines are an even 22 feet from the center of the basket, and on the arc, the distance is 23 feet and nine inches.
Starting at the baseline and running 28 feet toward the center of the court, a line bounds the team bench area. The line also acts as the starting place for inbounds passes after timeouts and fouls.
WNBA Basketball Court Dimensions
The Women’s National Basketball Association or WNBA’s court dimensions are identical to the NBA court in every way except the three-point line. Instead, the distance is equal to the International Basketball Federation (FIBA) at 22.15 feet from the center of the hoop. WNBA teams share arenas and playing surfaces with the NBA, which is why it’s no wonder the court dimensions are so similar.
NCAA Basketball Court Dimensions
National Collegiate Athletic Association or NCAA basketball courts have similar dimensions to the NBA and WNBA, which include the:
Court
Foul line
Backboard
Basket height
Tip-off circle
That said, there are a few significant differences in the dimensions of the NCAA court. For starters, the key is only 12 feet wide, rather than 16. The first box on the side of the key is only six feet from the baseline, not seven. The restricted area under the basket is also one foot smaller, at three feet in diameter rather than the NBA’s four.
However, the most recognizable difference between the NBA’s court dimensions and the NCAA’s is the distance of the three-point line. The NCAA three-point line is only 20 feet, nine inches from the center of the basket. Because of the smaller diameter, it is a continuous arc from one side of the baseline to the other, with no straight lines necessary to create space on the sidelines.
The difference in three-point line distances is the biggest adjustment for shooters to make as they begin their professional careers, and also why it’s so difficult to project how well a player will shoot in the pros.
High School Basketball Court Dimensions
High school basketball courts are a little different from their college and professional counterparts. The most noticeable difference is that the court is a full 10 feet shorter, measuring only 84 feet. However, there are some similarities. The court is still 50 feet wide. The basket is also 10 feet off the ground.
The tip-off circle has a six-foot radius, just like the big kid courts, and while the high school landscape isn’t as standardized as college and professional basketball, the backboard is supposed to have the same measurements as the NCAA and NBA.
Just as in college and professional basketball, the foul line is 15 feet from the backboard, and the key is 19 feet long. It’s also the same 12 feet wide as the NCAA — four feet narrower than the NBA and WNBA.
The other visible difference is the distance from the three-point line. Shorter than either the NCAA or NBA, the high school free throw line is just 19 feet, nine inches from the center of the basket. Additionally, high school basketball courts do not have any restricted area under the basket, since that rule doesn’t exist in high school basketball.
FIBA Basketball Court Dimensions
FIBA governs international basketball courts. The measurements for FIBA basketball courts differ from U.S. courts because of the difference between our Imperial measurements — feet and inches — and the more standard metric system.
FIBA courts are an even 28 meters long, which converts to almost 92 feet. The 15-meter width converts to just over 49 feet. The tip-off circle is a bit smaller as well, at 3.5 meters in diameter. This difference translates to a radius of about five feet, seven inches.
The key is almost the same size at 5.8 meters long and 4.8 meters wide. These numbers convert to within a few inches of 19 and 16 feet. The basket is 1.2 meters, or almost four feet, in from the baseline, which puts the foul line at 4.6 meters — 15 feet — away. The restricted area under the basket is 1.25 meters or just a shade more than four feet in radius.
The basket is still 10 feet off the ground, which means the biggest difference is the three-point line. At the top of the arc, the three-point line is 6.75 meters from the center of the basket or 22.15 feet. This measurement works out to about 22 feet, two inches. The FIBA three-point line, which has also been adopted by the WNBA, is over a foot and a half closer than the NBA line.
The History of Basketball Court Dimensions
Since its invention in 1891, basketball’s court dimensions have varied. Let’s look at some of its historical changes, as well as answering that nagging question — “Why are basketball hoops 10 feet high?” — below:
The Story Behind the 10-Foot High Hoop
It would appear the 10-foot basketball hoop is the result of a careful calculation that considers the human anatomy and mechanics of the game. After all, even the tallest players today have to jump to dunk a ball, and a ten-foot high rim gives a comfortable target to shoot for at a distance. But as we see so often in history, the truth is much more mundane.
When James Naismith dreamed up the game in Springfield, MA in 1891, the railing he chose to hang the baskets on was ten feet off the ground. So, while everything else about the sport has changed since that first game, the baskets are still right where Dr. Naismith hung them.
The History of the Three-Point Line
The three-point line is arguably the most recognizable aspect of a basketball court’s dimensions and part of the reason why is attributed to the history surrounding this semicircle.
The first instance of the three-point line appeared in the American Basketball League in 1961, a full 70 years after Dr. Naismith invented the game. The line was added to increase excitement, but the league folded in just one and a half seasons, so the idea never had a chance.
In 1967, the next competitor to the NBA arrived. The American Basketball Association, or ABA, instituted the three-point line from the very start, and it was a huge success. The ABA had many exciting innovations that produced a better product for the fans. But ultimately, there was not enough room for two professional basketball organizations, so the NBA and ABA merged in 1976.
The three-point line, however, was not included in the merger! The decision-makers in the NBA at the time were too stubborn to adopt such a radical change. They held out for three years before implementing the three-point line in the 1979-1980 season. The NCAA didn’t integrate it until 1986, and it didn’t arrive on high school basketball courts until 1987.
That isn’t the end of the story, however. The line was moved closer for three seasons in the ‘90s to try to boost scoring, but it was quickly moved back to its original place. Taking the idea to the extreme, the NBA has even admitted to having discussions about a four-point line. Ultimately, we’ll believe it when we see it.
The Original Cage Matches
In the early days of professional basketball, the game was played inside an actual cage. The reasons were more about practicality than about safety. The rule for who got to inbound a ball that left the court was “whoever got to it first,” so organizers took to putting up a cage so the ball could never go out of bounds in the first place.
Those first basketball courts were about a third smaller than they are today, and the cages provided a physical boundary and an extra immovable for savvy teams. Could you imagine how much different the game of basketball would be today if those cages had stuck around?
The Alternative Key Designs
Today, basketball courts at all levels share a common design for the key — a rectangle measuring either 19 feet by 16 feet or 19 feet by 12 feet. However, this was not always the case. From the creation of FIBA in 1956 until 2010, the key was a trapezoidal design that was significantly wider at the baseline.
Another design of this feature is responsible for the name “key.” Have you ever thought about how a rectangular area under a basket got such a random name?
The reason is that the original area was much narrower, while the circle surrounding the free throw line was the same size. These two factors combined to create a shape that resembled an old-fashioned key. In 1951, the key was widened to 12 feet and later to the 16 feet we see now in the NBA and FIBA.
While the term lives on, time has erased any record of its design and original reference. And for the record, the official name for this feature is “free throw lane,” which isn’t a phrase many of us hear often.
And that’s a wrap on the history of basketball’s court dimensions.
Build Your Basketball Court With PROformance
Perhaps you don’t have 94 feet of flat asphalt or indoor floor space. Don’t worry, because residential half court setups can be just as fun. And whether you are looking to paint your court or apply a pre-made solution, sticking to the official dimensions will take your pickup games to the next level.
Take a look at our selection of goals, nets and accessories to bring your home’s court together. You’ll have a hard time dragging your kids off the court as they spend hours posting up like Boogie, slashing like LeBron and launching it from deep like Steph.
Home / All sports / Basketball size 7,6,5,3 (weight, diameter, pressure)
03/20/2020 All sports Leave a comment 25,381 Views
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Basketball size varies by league, governing body, and gender and age of students. Basketballs differ from each other in weight, pressure, circumference and material of manufacture. According to the official rules of the game, the game projectile must have a spherical shape, be made in orange and have 8 black inserts and seams.
The official size of a basketball is numbered 7, it has the following characteristics: weight (mass) is - 567-650 grams, circumference - 749-780 cm, atmospheric pressure - 0.56 - 0.63 kg / cm 2 . This is the largest ball, and now look at the rest in the table:
Size
Circumference (cm)
Weight (grams)
Pressure (kg/cm 2)
Where applicable
7
749-780
567-650
0.56 - 0.63
Professional Men's Basketball, Boys 14+
6
724-737
510-567
0.56 - 0.63
Women's professional basketball, girls 12+, boys 12-13
5
690-710
470-500
0.56 - 0.63
Boys and girls 10-11 years old
3
560-580
300-330
0. 56 - 0.63
Boys and girls 4-9 years
Pass the Basketball Test
Basketballs are made from natural leather or synthetic leather - the pressure is the same for all sizes. It is worth remembering that a correctly inflated ball of the correct size is important to ensure quality training and skill development for players of different ages.
For games held under the auspices of the International Basketball Federation (FIBA), the ball is inflated to air pressure so that when it falls onto the court from a height of 1.8 meters, it should bounce to a height of 1.2-1.4 meters (measured by the top of the game ball).
Indoor and outdoor basketballs
There are no differences between the versions of the game in terms of size, but there are other nuances regarding manufacturing. Indoor balls are made of genuine leather, and outdoor balls are made of rubber.
Leather basketballs intended for indoor use should not be used outdoors. Concrete or asphalt surfaces cause the leather to become rough and wear out quickly, eventually resulting in poor hand-ball contact. Also, some balls for playing inside are made of composite or synthetic leather, but their quality leaves much to be desired.
For outdoor play, manufacturers make balls with a rubber surface, as it is able to interact better with rough field surfaces. Rubber basketball will be a good choice for beginner players as it is much easier to control and develop skills.
Best Selling Basketball Brands
Basketball is very popular all over the world, which means that ball manufacturers do not have to sit idle, because they need to compete, create a quality product and, accordingly, make a profit. Here are the 3 best selling basketball brands in the world.
Spalding (USA)
Wilson (USA)
Molten (Japan)
Spalding makes balls for the most popular league in the world, the NBA. Wilson is in demand with the NCAA and most of the youth leagues in the United States of America. But Molten is the main supplier of game equipment for FIBA tournaments, European championships and even the Olympic Games.
Note that on average for men, a standard size 7 basketball sells for $30-60.
Basketballs have changed a lot since the beginning of the game in the late 19th century. Today, technology has made it possible to make very high-quality and even smart balls. This was not always the case, because decades have passed and the balls have undergone many changes and improvements, although at the very beginning, James Naismith, the founder and father of basketball, used a soccer ball to play, which his students threw into peach baskets.
A new wave of basketball ball design, sweat throughout the appearance, will stand out flawless technology. This applies to the panels of the game projectile - now there are 8 of them, and the new composite structures have only two. New modern balls are constantly advertised by manufacturers. There are those that can control humidity, have more pimples - dots, and are even able to track the entire process of the game and in live mode and send information (strength of throw, rotation, impact) to Android or iPhone. Such a ball is 94Fifty.
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Determination of the force with which a basketball must be thrown to hit the basket
St. Petersburg
Kolpino
2019
Contents
Contents 2
Introduction. 3
Basketball as a sport game. 4
Elements of basketball studied in the study. 4
Determination of the overall study plan. 5
Progress. 6
Determining the acceleration time of the ball. 6
Determining the speed of the ball as it takes off. 8
Determining the angle of the ball. 9
Determine the acceleration of the ball. 10
Determining the mass of the ball. 10
Determination of the force with which the ball must be thrown to hit the basket. 10
Data analysis. 11
References. 14
Appendix. 15
Introduction.
One of my hobbies is playing basketball. The most spectacular element of the game is considered to be hitting the ball into the basket, especially from a long distance. Studying the laws of mechanics in a physics lesson, I had a question: “With what parameters do you need to throw the ball so that it hits the ring exactly?”. After searching for information on this topic on the Internet, I found several articles. The works [4,5] describe the throw technique, training methods, but there are no mechanical characteristics of the throw. The paper [2] defines the speed and angle of the ball when thrown from different points of the court. In the same place, these values are determined experimentally. The determination of the force with which the ball must be thrown was not made. I set myself the task of repeating the experimental determination of the speed and angle of the ball and calculate the force with which the ball must be thrown.
Purpose of work:
Determine the force with which it is necessary to throw a basketball in order for it to hit the basket.
Tasks:
Read and study the literature on the issue under study.
Experimentally determine the speed of the ball at the time of its departure, the angle of departure, the acceleration time, the mass of the ball.
Analytically determine the force with which the ball must be thrown.
Complete the work in accordance with the rules.
Prepare a presentation of the work.
Prepare a report for the presentation.
Compare findings with results from other studies.
Basketball as a sport game.
Basketball is one of the most popular sports in the world. This sport appeared in the USA in 1891. During the winter, the students of the Springfield Youth Christian Association College were very bored in physical education classes, as they had to do the same gymnastic exercises. And 21 December 1891 year old college teacher James Naismith found a way out of this situation. He tied two peach baskets to the balcony railing of the gymnasium and divided the students into two teams. The essence of the game was to throw more balls into the opponents' basket.
Basketball has been an Olympic sport since 1936, World Championships since 1950, European Championships since 1935.
Men's and women's national teams of the USSR - one of the strongest teams in the world for 1950-1980s. The achievements of the Russian national teams are not great, like their predecessors, but these teams have something to be proud of.
Basketball clubs of the country take part and become winners in the VTB United League, Euroleague, Eurocup, FIBA Challenge Cup. Under the leadership of the Basketball Federation of the Russian Federation, within the framework of the country, between the teams of basketball clubs, a men's championship is held in three leagues and a women's championship in four leagues, the national championship between teams of children's sports schools in different age groups.
Elements of basketball studied in the study.
Basketball is a complex, team game consisting of many elements. The main components of basketball are: gestures of referees, dribbling, passing the ball, rebounds, interceptions, block shots, throw. It is difficult to single out the most important element in the game, but getting the ball into the ring is the most anticipated moment, since this is the goal of the game. Therefore, for study, we chose a throw. Considering this component of the game, it is possible to distinguish 3 parts in it: the acceleration of the ball, the moment the ball is released from the hand and the flight of the ball into the basket.
In order to determine such mechanical parameters as the angle of the ball, its speed and the force with which it must be sent to the basket, it is necessary to mathematically describe the studied components of the throw. Considering the acceleration of the ball, we will be interested in the time for which the ball accelerates before departure. We will need it later when calculating the acceleration. The moment the ball leaves the hand will help to reveal the speed at which the ball is moving, which is necessary to determine the acceleration. Also, this moment will be needed when determining the angle of departure of the ball. The phase of the ball flight to the basket is of no interest for revealing the studied mechanical parameters. For these measurements, we used the following tools: a video camera (for recording a real throw), a GIMP graphics editor (for processing the resulting video sequence), scales, and a tailor's centimeter.
Determining the overall study plan.
To determine the required parameters, let's shoot a video of a basketball throwing into a basket. A similar method is described in [1]. To determine the force with which you need to throw the ball, we will use Newton's second law, which states: "The acceleration of a body is directly proportional to the force applied to the body, and inversely proportional to its mass" [3]. Hence, the force acting on a body is equal to the product of the mass of this body and the acceleration created by the force applied to this body. Accordingly, it is necessary to find the acceleration and mass of the body, i.e., in our case, the basketball.
We will determine the mass of the ball using weights. Acceleration is determined by dividing the speed of the ball by the acceleration time. To determine the speed, we need to know the distance that the ball travels after the ball has left the ball in a certain time. We will get these data by measuring the distance between the images of the ball on two adjacent frames, corresponding to the separation of the ball from the hand. We get the speed by dividing the distance by the time between frames - 1/25 s. The acceleration time is determined using the video sequence decomposed into frames, multiplying the number of frames by the frame rate of 1/25 s.
The resulting force will be the resultant of two forces: the force of gravity and the muscle force of the player. The muscle strength of the player is defined as the difference between the vectors of gravity and the resultant force obtained as a result of the experiment. To determine the module of muscle strength, we need the ball departure angle, which we will determine when processing the same frames as for determining the speed. In this case, the angle at which the player must throw the ball will be greater than the angle of the ball. The value of this angle is determined by calculation.
For the reliability of the obtained values, we will process several ball throws. As a result, we will use the average value.
Progress.
Determining the acceleration time of the ball.
In the course of the study, a video was made of ten throws of the ball into the ring by a player of the school team born in 2003. At the same time, a high-quality throw, when the ball hit the ring exactly, turned out to be only one. In other cases, the ball hit the ring after hitting the bow or backboard, or not hit at all. In the game it does not matter, but to determine the parameters of an accurate throw, such data cannot be used. Therefore, it was not possible to collect statistics as a result of the experiment. Further, in the calculations, the parameters of one accurate and three inaccurate throws were used. The measurement results and calculated values were recorded in the application table.
The acceleration time of the ball, as noted above, is a necessary parameter for calculating the acceleration, which in turn is needed to determine the force with which the ball is thrown into the basket. To determine this parameter, following the research plan, we filmed several shots of a basketball player from free throw distance using a video camera. The camera was located perpendicular to the throw plane for the minimum calculation error. After shooting, we decomposed the resulting video sequences into separate frames. It is worth considering that the time difference between each frame is 1/25 (s). Having a storyboard of video fragments of throws, we have chosen only those frames that are between the frame of the beginning of the ball acceleration and the frame of the ball departure, Figure 1.
Fig.1
It is worth noting that during the processing of frames, an inaccuracy in the resulting image was revealed: the ball was “blurred”. This is due to shooting errors (camera instability), with the peculiarities of the jpg image format in which the frames were recorded and the low resolution of the existing camera. Considering one of the causes of "blurring" - the jpg image format, it can be noted that it saves data with lossy quality. The image is divided into blocks of 8 by 8 pixels and averaged values are recorded for each of these blocks [7]. But this factor influenced what happened less than the other two: the instability of the camera and its low resolution. But it is quite difficult to achieve the best with the available equipment.
Returning to the course of the study, it can be noted that in order to calculate the acceleration time of the ball, we need to know the number of frames received over the range specified above. We calculated this value for each throw and entered it in column 7 of the application table. Now the results obtained must be multiplied by 1/25 (s) - the time elapsed between each frame of shooting, as noted above. And as a result, we got the acceleration time of the ball for each throw and put it in column 8 of the table. In the case of a successful throw, the number of frames was 21, the acceleration time was 0.84 s.
Determining the speed of the ball as it takes off.
The speed of the ball at the time of its departure, as mentioned above, is one of the necessary quantities to find the force with which it is necessary to throw the ball to hit the basket. To determine it, we, as well as when determining the acceleration time of the ball, used video fragments of a basketball player throwing a basketball into the basket, decomposed into frames.
We processed the video clips of all the throws: we took two adjacent frames after the ball took off (because in this section of the ball’s movement its speed is the highest, because then it will decrease due to air resistance and gravity) and cut out in each of them ball image, after which we connected the centers of the resulting circles with a line and saved the resulting images in jpg format, as shown in Figure 2.
Fig.2
Now we had to calculate the distance that the ball flew in this 1/25 (s) from the received images. To do this, we used the built-in tool of the GIMP graphics editor "meter". For each image, we measured the length of the resulting lines and entered the results in column 4 of the table.
But this data shows the distance from the center of the circle of one ball to the center of the circle of the other ball specifically in the figure in millimeters. In order to find out the actual flight length, it is necessary to find the proportionality factor between the measurements in the image and the measurements in the real world. We decided to find this coefficient through the ratio of the diameter of a real basketball to the diameter of the ball in the picture. To do this, we measured the diameter of a real basketball using the formula S=πd, hence d=S/π. Taking a tailor's centimeter, we measured the circumference of the ball, after which we divided the resulting value by the number π. The resulting value d \u003d 0.744 / π \u003d 0.237 m
Now we only need to measure the diameter of the ball in the image. We did this with the help of the GIMP graphical editor's "meter" tool. Using the data obtained, the proportionality coefficient is easily found: k=0.237/0.0252=9.4. Multiplying the resulting coefficient by the length of the path traveled by the ball in 1/25 s after departure, we get the real path of the ball. For each throw, these values were calculated and entered in column 5 of the table. In the case of a successful throw, the distance traveled in 1/25 s was 0.249m. To determine the speed of the ball, it is necessary to divide the results obtained by 1/25 s. Ball speeds were also entered in column 6 of the table. For a successful throw, the speed was 6.23 m/s
Determination of the ball departure angle.
To determine the angle of departure for each throw, we used the previously obtained images of the movement of the ball for 1/25 (s) after it left the hand, as shown in Figure 2. Now we worked on these images in the GIMP graphics editor using the " Meter". It should be noted that the values of the angle of departure of the ball obtained for each throw are measured relative to the horizon. So, we entered the resulting values of the angles of departure of the basketball in column 3 of the table. The effective throw was made at an angle of 570.
Determining the acceleration of the ball.
Detecting the ball's acceleration is the penultimate step in determining the force with which the ball must be thrown to hit the basket. In order to calculate it, we had to substitute the previously obtained values into the formula a = . But since v0=0 m/s (because for a body at rest acceleration starts from 0 m/s), the formula becomes a=. And we see that we have enough data to determine the acceleration of the ball for each throw. We made calculations and entered the obtained data in column 9tables. Acceleration during a successful throw was 7.4 m/s2.
Determining the mass of the ball.
The final step to determine the force with which you need to throw a basketball to hit the basket is to determine the mass of the ball. It should be noted that for the experiment we used a ball that complies with the FIBA rules [6]. We used scales to determine its mass. They showed us a value of 0.617 kg. We now had a complete set of data to get the force applied to the ball for each throw.
Determination of the force with which the ball must be thrown to hit the basket.
The resultant force is obtained by multiplying the acceleration by the mass of the ball. The values for all throws are listed in column 10 of the table; for a successful throw, the force was 4.58N. The muscle force applied to the ball is defined as the vector difference between the resultant force and the force of gravity, Figure 3.
Fig.3
The modulus of the applied force is determined by the cosine theorem:0003
For a successful throw Fp=10.2N, all values are in column 10 of the table.
The angle at which the player must throw the ball will be equal to the sum of the angle of departure and the angle between the vectors of the resultant force and the applied force :
= 760. That is, in order for the ball to fly out at an angle of 570, it should be thrown at an angle of 760.
Analysis of the obtained data.
In order to fully verify the correctness of our calculations, we decided to compare our results with the results obtained in other works [2]. In the work, the speed of the ball was analytically calculated at the moment of separation of the basketball from the hand when throwing from a distance to the ring in the range from 4 to 6 meters, and in our study, the distance was 3 meters. Therefore, we independently determined the theoretical value of the departure speed using the formulas given in the mentioned work:
v= (3)
where
g is the acceleration due to gravity, 9.81;
α- departure angle, ;
β - the minimum angle of approach of the ball, at which it is possible to hit the ring, 320;
h - vertical distance from the departure point to the ring, 0.7 meters;
l - horizontal distance to the ring, 3 meters.
= 480
v = 6.1
The values of the take-off angle 570 and velocity 6.2 obtained as a result of the experiment agree with the analytically obtained values.
The resulting force with which to throw the ball into the ring is greater than the force of gravity, because as a result of its action, the energy necessary to reach the ring located at a height of 3.05 meters from the floor level is achieved. The value of strength is negligible for the muscular capabilities of a person, which allows even children to play basketball. And the accuracy of the throw depends on the technique, the accuracy of determining the distance to the ring and other factors, which together are called the feeling of the throw. The same sense of throw should include the definition of the angle of throw, at which the ball will fly at a different angle along the required trajectory. This fact was not considered in the textbooks on teaching the game of basketball, most likely due to the intuitive definition of the necessary movement of the hand during the throw. In real conditions, the accuracy of the throw is achieved by multiple repetitions of the required movement.
The values obtained as a result of the study can be useful in the development of a robot-basketball player, the meaning of which is to popularize the achievements of science and technology.
Plans for the development of this study are to conduct more accurate measurements and collect statistical data necessary to ensure the reliability of the results.
References.
Vlasov A.A. The use of video filming in teaching to throw the ball in basketball / A.A. Vlasov, V.A. Solodyannikov [Electronic resource] // Electronic periodical scientific journal "SCI-ARTICLE.RU". 2016. No. 38. pp. 66-70. - access mode: http://sci-article.ru/number/10_2016.pdf - Download. from the screen
Vlasov A.A. Determination of the allowable departure angle and ball speed when throwing a basketball into the basket / A.A. Vlasov [Electronic resource] // Electronic periodical scientific journal "SCI-ARTICLE.RU". 2016. No. 38. pp. 70-80. - access mode: http://sci-article.ru/number/10_2016.pdf - Download. from screen
Physics. Grade 8: textbook. for general education organizations with app. to an electron. media / V.V. Belaga, I.A. Lomachenkov, Yu.A. familiarity; Russian Academy of Sciences, Russian Academy of Education, Prosveshchenie Publishing House. - 2nd ed. – M.: Prosveshchenie, 2014- 159s Sport games. Technique, teaching tactics. Textbook for students of higher pedagogical educational institutions. / Ed. Yu.D. Zheleznyak, Yu.M. Portnova. - M .: Publishing Center "Academy", 2001. - 520 p.
Cousy, B. Basketball: concepts and analysis / B. Cousy, F. Power, abridged translation from English. E. R. Yakhontova. - M .: Physical culture and sport, 1975 - 270 p.
Official Basketball Rules. FIBA 2014, Barcelona, Spain, 2014.
JPEG graphic format - description and compression algorithms0002 Source: http://matrixblog. ru/2015/03/22/graficheskij-format-jpeg-opisanie-i-algoritmy-szhatiya/
Appendix.
Table.1
No.
Throw
Result
Voil angle, Grad
Distance between balls, M
Real, M
Real District
speed, m/s
Summary of the acceleration cadres
Acceleration time, with
Acceleration, m/s2
Estimated force, N
APPLICAL
City of the Throw, City of the City, City of the City, Came
Same goes for the WNBA. In FIBA, it’s 16.08 feet wide. At the NCAA level, the key is 12 feet wide. High school and junior high school use the same size key as the NCAA.
21 feet wide.
At the junior high, high school, NCAA, WNBA and NBA levels, the free-throw line is 15 feet away from this point. At the FIBA level, the free-throw line is actually a bit further—15.09 feet from the point.
We play baseball across parts of the globe, but we play basketball worldwide. You can play with as few as two people and as many as ten. Shoot hoops indoors and outdoors and on any surface hard or flat enough to bounce a ball.
The outer dimensions are 94 feet long by 50 feet wide. The half court line is, as the name would suggest, halfway between each end line. In the middle of the half court line is a tip-off circle with a six-foot radius, which often sports the home team’s logo.
If a defender is inside this semicircle, he cannot draw a charging foul. Along both sides of the key, lines are drawn three feet apart to create the standing positions for other players during a free throw attempt, starting with a box that is seven feet from the baseline and one foot wide.
Instead, the distance is equal to the International Basketball Federation (FIBA) at 22.15 feet from the center of the hoop. WNBA teams share arenas and playing surfaces with the NBA, which is why it’s no wonder the court dimensions are so similar.
The NCAA three-point line is only 20 feet, nine inches from the center of the basket. Because of the smaller diameter, it is a continuous arc from one side of the baseline to the other, with no straight lines necessary to create space on the sidelines.
The tip-off circle is a bit smaller as well, at 3.5 meters in diameter. This difference translates to a radius of about five feet, seven inches.
Let’s look at some of its historical changes, as well as answering that nagging question — “Why are basketball hoops 10 feet high?” — below:
However, this was not always the case. From the creation of FIBA in 1956 until 2010, the key was a trapezoidal design that was significantly wider at the baseline.
Don’t worry, because residential half court setups can be just as fun. And whether you are looking to paint your court or apply a pre-made solution, sticking to the official dimensions will take your pickup games to the next level.
56 - 0.63 
Concrete or asphalt surfaces cause the leather to become rough and wear out quickly, eventually resulting in poor hand-ball contact. Also, some balls for playing inside are made of composite or synthetic leather, but their quality leaves much to be desired. 
Wilson is in demand with the NCAA and most of the youth leagues in the United States of America. But Molten is the main supplier of game equipment for FIBA tournaments, European championships and even the Olympic Games. 
New modern balls are constantly advertised by manufacturers. There are those that can control humidity, have more pimples - dots, and are even able to track the entire process of the game and in live mode and send information (strength of throw, rotation, impact) to Android or iPhone. Such a ball is 94Fifty. 
5 
The paper [2] defines the speed and angle of the ball when thrown from different points of the court. In the same place, these values are determined experimentally. The determination of the force with which the ball must be thrown was not made. I set myself the task of repeating the experimental determination of the speed and angle of the ball and calculate the force with which the ball must be thrown. 
We get the speed by dividing the distance by the time between frames - 1/25 s. The acceleration time is determined using the video sequence decomposed into frames, multiplying the number of frames by the frame rate of 1/25 s. 
The camera was located perpendicular to the throw plane for the minimum calculation error. After shooting, we decomposed the resulting video sequences into separate frames. It is worth considering that the time difference between each frame is 1/25 (s). Having a storyboard of video fragments of throws, we have chosen only those frames that are between the frame of the beginning of the ball acceleration and the frame of the ball departure, Figure 1. 
But this factor influenced what happened less than the other two: the instability of the camera and its low resolution. But it is quite difficult to achieve the best with the available equipment. 
To determine it, we, as well as when determining the acceleration time of the ball, used video fragments of a basketball player throwing a basketball into the basket, decomposed into frames. 
In order to find out the actual flight length, it is necessary to find the proportionality factor between the measurements in the image and the measurements in the real world. We decided to find this coefficient through the ratio of the diameter of a real basketball to the diameter of the ball in the picture. To do this, we measured the diameter of a real basketball using the formula S=πd, hence d=S/π. Taking a tailor's centimeter, we measured the circumference of the ball, after which we divided the resulting value by the number π. The resulting value d \u003d 0.744 / π \u003d 0.237 m 
In the case of a successful throw, the distance traveled in 1/25 s was 0.249m. To determine the speed of the ball, it is necessary to divide the results obtained by 1/25 s. Ball speeds were also entered in column 6 of the table. For a successful throw, the speed was 6.23 m/s 
In order to calculate it, we had to substitute the previously obtained values into the formula a = . But since v0=0 m/s (because for a body at rest acceleration starts from 0 m/s), the formula becomes a=. And we see that we have enough data to determine the acceleration of the ball for each throw. We made calculations and entered the obtained data in column 9tables. Acceleration during a successful throw was 7.4 m/s2. 
The values for all throws are listed in column 10 of the table; for a successful throw, the force was 4.58N. The muscle force applied to the ball is defined as the vector difference between the resultant force and the force of gravity, Figure 3. 
Therefore, we independently determined the theoretical value of the departure speed using the formulas given in the mentioned work: 
And the accuracy of the throw depends on the technique, the accuracy of determining the distance to the ring and other factors, which together are called the feeling of the throw. The same sense of throw should include the definition of the angle of throw, at which the ball will fly at a different angle along the required trajectory. This fact was not considered in the textbooks on teaching the game of basketball, most likely due to the intuitive definition of the necessary movement of the hand during the throw. In real conditions, the accuracy of the throw is achieved by multiple repetitions of the required movement. 
for general education organizations with app. to an electron. media / V.V. Belaga, I.A. Lomachenkov, Yu.A. familiarity; Russian Academy of Sciences, Russian Academy of Education, Prosveshchenie Publishing House. - 2nd ed. – M.: Prosveshchenie, 2014- 159s Sport games. Technique, teaching tactics. Textbook for students of higher pedagogical educational institutions. / Ed. Yu.D. Zheleznyak, Yu.M. Portnova. - M .: Publishing Center "Academy", 2001. - 520 p. 
ru/2015/03/22/graficheskij-format-jpeg-opisanie-i-algoritmy-szhatiya/ 
