Parabolas and Sports By Valerie Belew History of

Parabolas and Sports By, Valerie Belew

History of Parabolas • Menaechmus (380 BC - 320 BC) found the parabola • Apollonius (262 BC - 190 BC) named the parabola • Pappus (290 - 350) found the focus and directrix of the parabola • Galileo (1564 - 1642) saw that objects falling due to gravity due so in parabolic paths • Gregory (1638 -1675) studied properties of the parabola • Newton (1638 - 1675) studied properties of the parabola

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 = 4 p(x-h) • Standard Form when directrix is parallel to the x-axis: • (x-h)² = 4 p(y-k)

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.

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

Increasing Your Chances of Making a Shot • 1980 s, 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.

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 13. 75 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.

Video • https: //www. youtube. com/watch? v=HOi. H 1 e. VCggw

Bibliography Highnessfsk. "Sport Science: Stephen Curry. " You. Tube, 15 May 2013. Web. 06 Apr. 2016. https: //www. youtube. com/watch? v=HOi H 1 e. VCggw "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. The. Washington Post Company, 16 Mar. 2010. Web. 5 Apr. 2016.