Mrs. MerrillPhysics

Feb 14,2007Andrea Villegas, Sunri Yu

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

The ProcedureThere 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.

Applying Physics to BasketballThe 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

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

Separate the motion into 2 parts:

• x (horizontal) : 1. Uniform motion:

acceleration is 02. Initial velocity: V0x

3. Use cosine (x value)

4. Expression for the displacement as a function of time: x= △Vx0 t = (V0 cos ∂0) t

• y (vertical)1. Free fall: -g = -9.8

m/s².2. Initial velocity: V0y

3. Use sine (y value)4. Expressions with

time:

1. Vy = Vy0 – gt

2. △y= Vy0 t - ½g t²

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?

Free-Throw Chart: Big G 　 　

　 　 　

Height 7 feet 2.13 meters

Distance from Basket 15 feet 4.57 meters

Launch Speed 20 mph 8.94 m/s

Angle (degrees) 69.8 69.8

Moving Speed of Ball 17.71 mph 7.92 m/s²

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 = △ V0x t5. 15 feet = 3.08 (t)6. t = 15 / 3.087. t = 4.87 s8. Yes, he makes it

within 5 seconds

Free Throw Chart for Big G

Free-Throw Chart: Big G feet & 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

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

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)

Bibliography/Credit1. 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/archives0506/021606.html&h=484&w=329&sz=115&hl=en&start=39&tbnid=XfcDIv7Od1PUSM:&tbnh=129&tbnw=88&prev=/images%3Fq%3Dbasketball%2B%2Bfree%2Bthrow%26start%3D20%26ndsp%3D20%26svnum%3D10%26hl%3Den%26rls%3DGGLG,GGLG:2005-39,GGLG:en%26sa%3DN

4. http://www.pserie.psu.edu/athletics/wbball/images/slomski%20free%20throw%202005-06.JPG

5. http://www.newtonrec.org/Boys%20Free%20Throw%2001.75.jpg6. http://www.usabasketball.com/images/2004/04_ymwcq_may-free-throw.jpg