1. Parabolas and Sports
By,
Valerie Belew

2. History of Parabolas Menaechmus (380 BC - 320 BC) found the parabola
Apollonius (262 BC BC) named the parabola
Pappus ( ) found the focus and directrix of the parabola
Galileo ( ) saw that objects falling due to gravity due so in parabolic paths
Gregory ( ) studied properties of the parabola
Newton ( ) studied properties of the parabola

3. Parabolas Definition:
A parabola is a set of all points that are the same distance from a fixed line (directrix) and a fixed point (focus)not on the directrix
Equation:
Standard Form when directrix is parallel to the y-axis:
(y-k)² = 4p(x-h)
Standard Form when directrix is parallel to the x-axis:
(x-h)² = 4p(y-k)

4. General Rules for Parabolas
When p is positive, the parabola opens upwards
When p is negative, the parabola opens downwards
When h is negative, it moves to the left of the orgin. When h is positive, it moves to the right of the orgin.
When k is negative, it moves towards the bottom of the graph. When k is positive, it moves towards the top of the graph.

5. Parabolas in Basketball
The hoop is 18 inches in diameter, and the men's ball is about 9.5 inches wide (women's about 9.2)
angle of 90 degrees to the horizontal hoop rim gives 4.25 inches of free space all around
At 55 degrees, it's about 2.5 inches
At 45 degrees, it's down to 1.5 inches.
At 30 degrees, it's basically impossible to get the ball straight into the basket

6. Increasing Your Chances of Making a Shot
1980s, Peter Brancazio, then a physics professor at Brooklyn College, determined that adding two feet to the height at which a shot leaves the player's fingers increases the success rate by a whopping 17 percent. No wonder you see so many jump shots.
the most distance with the least effort by firing a projectile at 45 degrees, exactly midway between vertical and horizontal.
The reason is that 45 degrees is the ideal least-effort angle only if the ball is shot from the same height as the basket, which is 10 feet above the floor.
Brancazio explains that you need 45 degrees plus half the angle formed by a straight line between the position of the ball at launch and the basket. Depending on your height and where you are on the court, that typically ranges from 7 to 14 degrees.

7. Continued…
For most players at a distance of 10 to 25 feet, the least-effort angle ranges between 47 and 52 degrees.
Using that system, you can calculate the ideal free-throw angle. It's feet from the free-throw line to the center of the basket, and a 6-foot player launches the ball from about seven feet above the hardwood. That works out to a shooting angle of 51 degrees.

8. Video

9. Bibliography
Highnessfsk. "Sport Science: Stephen Curry." YouTube. YouTube, 15
May Web.06Apr
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"History of the Parabola." Parabola Project. N.p., n.d. Web. 5 Apr. 2016
"In Basketball, Shooting Angle Has a Big Effect on the Chances of Scoring.“
Washington Post. TheWashington Post Company, 16 Mar Web.
5 Apr