2. Mrs. Merrill Physics Feb 14,2007 Andrea Villegas, Sunri Yu

3. What is a Free Throw? Free Throw: In a basketball game when a player fouls another player, the player fouled on is rewarded with a ‘free throw’. Also known as the Foul Shot

4. The Procedure There is nothing simpler in basketball than making a free throw. Why? 1.You stand exactly 15 feet from the basket. 2.You have all the time the referee gives you. 3.There is no one blocking your view.

5. Applying Physics to Basketball The Physics of a Free Throw: Projectile Motion Key to a successful free throw depends on… -The arc: the higher the better - means more of a chance scoring. -The angle of ball. -Correct launch speed. -Your aim. -The most ideal shot: When the ball goes straight down into the basket, like this 

6. Basketball in Projectile Motion Remember: 1.The ball moves in both the x and y direction- This is called moving in two dimensions 2.The acceleration in the y direction is –g, just like in free fall. (–g = -9.8 m/s²) 3.Air resistance is neglected: acceleration in the x direction is 0. 4.Ignore the rotation of the earth

7. Separate the motion into 2 parts: x (horizontal) : 1.Uniform motion: acceleration is 0 2.Initial velocity: V 0x 3.Use cosine (x value ) 4.Expression for the displacement as a function of time: △ x= V x0 t = ( V 0 cos ∂ 0 ) t y (vertical) 1.Free fall: -g = -9.8 m/s². 2.Initial velocity: V 0y 3.Use sine (y value) 4.Expressions with time: 1.Vy = V y0 – gt 2. △ y= V y0 t - ½g t²

8. Experiment Part 1: Big G is about to make a free throw:. He stands 7 feet tall, 15 feet away from the basketball hoop. The ball’s launching speed is 8.94 m/s Angle is 69.8 Does the ball go in?

9. Free-Throw Chart: Big G Height7 feet 2.13 meters Distance from Basket15 feet 4.57 meters Launch Speed20 mph 8.94 m/s Angle (degrees)69.8 Moving Speed of Ball17.71 mph 7.92 m/s²

10. Experiment Part 2: The referee only gives 5 seconds to shoot a free throw. Will the basketball go in within 5 seconds? 1.First, find V0x: 2.V0x= cos 69.8 V0= cos 69.8 x 8.94 = 3.08 m/s squared 3. Plug 3.08 in for V0x into this equation to find the time: 4. △ x = V 0x t 5. 15 feet = 3.08 (t) 6.t = 15 / 3.08 7. t = 4.87 s 8.Yes, he makes it within 5 seconds

12. Free Throw Chart for Big G Free-Throw Chart: Big Gfeet&meters Height (ft)7 feet tall 2.13 meters Distance from Basket (ft)15 feet 4.57 meters Launch Speed (mph)20 mph 8.94 m/s Angle (degrees)68 degrees 69.8 degrees Result: Moving Speed of Ball (mph)17.71 mph 7.92 m/s²

13. Conclusion A free throw in basketball is a good example of projectile motion: The ball moves in 2 dimensions –X direction –Y direction a = 0 in the horizontal: air resistance is neglected. In the vertical, -g = -9.8 because it is a free fall You can use equations to find the time it takes for the basketball to go in

14. The 5 W’s of Website Research WHO: Who wrote the pages and are they an expert? Is a biography of the author included? How can you find out more about the author? WHAT: What does the author say is the purpose of the site? What else might the author hav ein mind for the site? What makes the site easy to use? WHEN: When was the site created? Last updated? WHERE: Where does the information come from? Where can I look to find out more about the producer/sponsor? WHY: Why is this information useful for my purposes? Why should I use this information? Why is this page better than another? Copyright 2001-2003 by Kathy Schrock (kathy@kathyschrock.net)

15. Bibliography/Credit 1.Encyclopedia: Zumerchik, John. “The Physics of Shooting.” Encyclopedia of Sports Science. Copyright 1997. 2.Website: Rist, Curtis. “The Physics of… Foul Shots. Why everyone in the NBAought to be using a granny shot from the foul line.” DISCOVER. October 2000. Discover Vol. 21 No. 10. Monday, February 12, 2007. http:/ /www.discover.com/issues/oct-00/departments/featphysics/ 3.Pictures: http://images.google.com/imgres?imgurl=http://hsujacks.com/images/washington %2520freethrow.gif&imgrefurl=http://hsujacks.com/wbasketball/archives0506/0216 06.html&h=484&w=329&sz=115&hl=en&start=39&tbnid=XfcDIv7Od1PUSM:&tbnh =129&tbnw=88&prev=/images%3Fq%3Dbasketball%2B%2Bfree%2Bthrow%26sta rt%3D20%26ndsp%3D20%26svnum%3D10%26hl%3Den%26rls%3DGGLG,GGL G:2005-39,GGLG:en%26sa%3DN 4.http://www.pserie.psu.edu/athletics/wbball/images/slomski%20free%20throw%202 005-06.JPGhttp://www.pserie.psu.edu/athletics/wbball/images/slomski%20free%20throw%202 005-06.JPG 5.http://www.newtonrec.org/Boys%20Free%20Throw%2001.75.jpghttp://www.newtonrec.org/Boys%20Free%20Throw%2001.75.jpg 6.http://www.usabasketball.com/images/2004/04_ymwcq_may-free-throw.jpghttp://www.usabasketball.com/images/2004/04_ymwcq_may-free-throw.jpg