Basketball, to me and others, is their favorite sport, whether it’s if you enjoy watching, playing, or even just knowing things about the game. For myself, I enjoy all of these things from: shooting the ball, to watching my favorite teams, to knowing the stats of my favorite players. Now, on the subject of the game, many people would always strive to get better at playing the game, if it’s in the aspects of: shooting, passing, dribbling, etc. For me, I would always try to figure out how to get better at shooting, if that had to do with my aim, accuracy, or my form in general. Then, I got to thinking what exactly are the aspects of creating the perfect shot, or at least a decent shot. I always knew that shooting a basketball involved math, I
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The rim of a basket has a diameter of 18 inches. The size of a basketball can vary. A women’s basketball can be from 8.5-9 inches, and a men’s basketball can be from 9.5- 10 inches. So let us assume that our player is a women or at least using that size of a ball for the rest of this paper.
For our question, we are interested in how close the center of the basketball is to the front of the rim and the back of the rim.
This is called a variation of an optimization problem in calculus, in other words we need to find the minimum distance from a point not on a curve to the curve. For the shot angle of 60 degrees, the equations of motion are:
The distance from the front of the rim is given by the minimum of
For Db, the distance from the back of the rim, 14.25 is changed to 15.75
The results would be Dfmin=7.77 inches and Dbmin=7.82 inches
The shot easily goes through the basket and being a nothing but net, with either basketball being …show more content…
After looking at other research papers that experimented with changing the initial velocity, there we found that with an initial speed of 23.56 ft/sec we would get Dfmin=4.49 inches and Dbmin=4.48 inches. Since in our scenario the radius of the ball would be 4.5 inches, so that means that the shot grazes the front and the back of the rim. This shows that it is not possible to make a nothing but net jump shot with an angle of 30 degrees as the angle of elevation from a distance of 15 feet and a height of 10 feet.
But now you might be thinking can we make a nothing but net shot with an angle of elevation of 30 degrees, how close to 30 degrees can we get?
So solving the equation for a shot that goes through the center of the basket but this time with an initial angle of 31 degrees we get:
,
,
,
So with these results we can understand that the ball clears the rim and the shot is nothing but net. So with the math of how to make a near perfect shot in basketball from a certain distances, we can understand that many things in life, like basketball, have math incorporated in them in one way or another. Math for certain things may be easier to understand than others, but knowing or not knowing the math doesn't necessarily mean that you’ll be better in that game than others. But from my very own experience, knowing the mechanics of a basketball
The rim of a basket has a diameter of 18 inches. The size of a basketball can vary. A women’s basketball can be from 8.5-9 inches, and a men’s basketball can be from 9.5- 10 inches. So let us assume that our player is a women or at least using that size of a ball for the rest of this paper.
For our question, we are interested in how close the center of the basketball is to the front of the rim and the back of the rim.
This is called a variation of an optimization problem in calculus, in other words we need to find the minimum distance from a point not on a curve to the curve. For the shot angle of 60 degrees, the equations of motion are:
The distance from the front of the rim is given by the minimum of
For Db, the distance from the back of the rim, 14.25 is changed to 15.75
The results would be Dfmin=7.77 inches and Dbmin=7.82 inches
The shot easily goes through the basket and being a nothing but net, with either basketball being …show more content…
After looking at other research papers that experimented with changing the initial velocity, there we found that with an initial speed of 23.56 ft/sec we would get Dfmin=4.49 inches and Dbmin=4.48 inches. Since in our scenario the radius of the ball would be 4.5 inches, so that means that the shot grazes the front and the back of the rim. This shows that it is not possible to make a nothing but net jump shot with an angle of 30 degrees as the angle of elevation from a distance of 15 feet and a height of 10 feet.
But now you might be thinking can we make a nothing but net shot with an angle of elevation of 30 degrees, how close to 30 degrees can we get?
So solving the equation for a shot that goes through the center of the basket but this time with an initial angle of 31 degrees we get:
,
,
,
So with these results we can understand that the ball clears the rim and the shot is nothing but net. So with the math of how to make a near perfect shot in basketball from a certain distances, we can understand that many things in life, like basketball, have math incorporated in them in one way or another. Math for certain things may be easier to understand than others, but knowing or not knowing the math doesn't necessarily mean that you’ll be better in that game than others. But from my very own experience, knowing the mechanics of a basketball