By Flipping Physics, 05/22/2014

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This is how you include air resistance in projectile motion. It requires the Drag Force and Numerical Modeling (or the Euler Method). It is also very helpful to use a spreadsheet to do the calculations. I prove a statement from a previous projectile motion problem video, "Air resistance decreases the x displacement of the ball by less than 1 cm."

Content Times:

0:22 The statement this video proves

1:01 The basic concept of air resistance

1:54 The Free Body Diagram

2:20 The Drag Force Equation

3:13 Information about the Lacrosse Ball

4:03 The Drag Coefficient

4:55 The Density of Air

5:18 How the Drag Force affects the motion

5:58 The basic idea of Numerical Modeling (or the Euler Method)

6:50 Solving for the acceleration in the x direction

8:53 Solving for the final velocity in the x direction

9:54 Solving for the final position in the x direction

11:41 Entering the Lacrosse Ball information into Excel

13:34 Solving for the Drag Force in x direction in Excel

14:29 Solving for the acceleration in the x direction in Excel

14:58 Solving for the final velocity and final position in the x direction in Excel

15:46 Solving for the acceleration in the y direction

17:21 Solving for all the variables in the y direction in Excel

19:13 Click and Drag Copy. Harnessing the Power of Excel!

19:43 Understanding the numbers in Excel

20:35 Solving for the decrease in the x displacement caused by the Drag Force

[url="http://www.flippingphysics.com/the-euler-method.html"]Want lecture notes & the Excel File?[/url]

(also contain's photo credits and links to website's shown in video)

The original problem videos for this are:

[url="http://www.flippingphysics.com/projectile-motion-problem-part-1-of-2.html"](part 1 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity[/url]

[url="http://www.flippingphysics.com/projectile-motion-problem-part-2-of-2.html"](part 2 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity[/url]

[url="http://www.flippingphysics.com/how-many.html"]How Many Attempts did it Really Take?[/url] - with live music from Amos Lee

[url="http://www.flippingphysics.com/give.html"]1¢/minute[/url]

Content Times:

0:22 The statement this video proves

1:01 The basic concept of air resistance

1:54 The Free Body Diagram

2:20 The Drag Force Equation

3:13 Information about the Lacrosse Ball

4:03 The Drag Coefficient

4:55 The Density of Air

5:18 How the Drag Force affects the motion

5:58 The basic idea of Numerical Modeling (or the Euler Method)

6:50 Solving for the acceleration in the x direction

8:53 Solving for the final velocity in the x direction

9:54 Solving for the final position in the x direction

11:41 Entering the Lacrosse Ball information into Excel

13:34 Solving for the Drag Force in x direction in Excel

14:29 Solving for the acceleration in the x direction in Excel

14:58 Solving for the final velocity and final position in the x direction in Excel

15:46 Solving for the acceleration in the y direction

17:21 Solving for all the variables in the y direction in Excel

19:13 Click and Drag Copy. Harnessing the Power of Excel!

19:43 Understanding the numbers in Excel

20:35 Solving for the decrease in the x displacement caused by the Drag Force

[url="http://www.flippingphysics.com/the-euler-method.html"]Want lecture notes & the Excel File?[/url]

(also contain's photo credits and links to website's shown in video)

The original problem videos for this are:

[url="http://www.flippingphysics.com/projectile-motion-problem-part-1-of-2.html"](part 1 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity[/url]

[url="http://www.flippingphysics.com/projectile-motion-problem-part-2-of-2.html"](part 2 of 2) An Introductory Projectile Motion Problem with an Initial Horizontal Velocity[/url]

[url="http://www.flippingphysics.com/how-many.html"]How Many Attempts did it Really Take?[/url] - with live music from Amos Lee

[url="http://www.flippingphysics.com/give.html"]1¢/minute[/url]