User:Vdviradiya/sandbox

'''Calculus In Basketball ID-201701266 '''

There is calculus everywhere.From,finance to sports,cycle to spaceship,there is calculus behind it.Here,We will know the use of calculus in Sports specially in Basketball. many years ago,basketball players struggled in their game for more improvement,but now a days,because of calculus and technology,players can easily improve their game with some basic application. Three Point Shot "A three-point shot is a goal in a basketball game that is made from beyond the three-point line, a designated arc surrounding the basket."

Arc: The Arc is the path the basketball flies from the time it leaves the shooter's hand until it arrives at the basket.After the shot,given the strength of release and the angle of release,a mathematician can accurately predict the [path and the arc length because Gravity is the only force affecting the ball.

if we want to make a perfect three point shot,we have to calculate arc length.

Hoop Margin: Hoop margin is the amount of open space left after the ball enter in the 18 inch ring of the hoop.If a ball enter directly from above,since a men's ball 9.7 inches in diameter,the hoop margin is 18-9.7=8.3 inches.

Apartment hoop margin is the apartment opening of the hoop to the ball.The flatter the arc,the smaller the ellipse.

Apartment hoop margin is the AH size minus the diameter of the ball.

Although the greatest AH margin and AH size is obtained when the ball travels a 55 degree arc,the actual optimal shot is for it to travel at a 45 degree arc.This is because at 55 degrees,it is proven significantly harder for the shooter to aim and release at that angle constantly without maintaining release strength.Nonetheless,professional athletes in the NBA have practiced and mastered their release to an angle closer to the 55 degrees to fully gain an advantage of the AH margin and AH size.

let's take r(t), a differentiable vector valued function that represent the position of a particle(here,Basketball).Then the speed of the particle is the magnitude of the velocity vector.In one variable calculus,we defined the acceleration of a particle as the second derivative of the positive function and Jerk is the third derivative.

if we divide arc into small divisions,we can say that all small divisions becomes linear.so,we can get length.so,we have to integrate it from ɖ to β .where ɖ is initial point and β is ending point.

By some of calculations,we can get suitable arc length and releasing angle.suitable arc length that we got is ≈40 ft. and appropriate angle for it is between 45 to 55 degree. with using some calculus, common man can also make a perfect shot like a great basketball player.Here, is the example:

click to see the Sweeper making perfect basketball shot with some calculations and measurement

About Commercialization

We can build an app which can be very helpful for basketball players to improve their game.this app get the values of players's height,players's distance and his releasing angle when he throws the ball and after getting values,algorithms that are set by maker do this type of calculus and display some useful information like what should your releasing angle and velocity of throwing ball and etc. etc.

So,We can commercialize this Use of Calculus in basketball.